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id="toc-Automorphisms-sublist" class="vector-toc-list"> <li id="toc-Construction_of_Lie_groups_via_diagram_automorphisms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Construction_of_Lie_groups_via_diagram_automorphisms"> <div class="vector-toc-text"> 7.1 Construction of Lie groups via diagram automorphisms </div> </a> <ul id="toc-Construction_of_Lie_groups_via_diagram_automorphisms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Folding" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Folding"> <div class="vector-toc-text"> 7.2 Folding </div> </a> <ul id="toc-Folding-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_maps_of_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Other_maps_of_diagrams"> <div class="vector-toc-text"> 8 Other maps of diagrams </div> </a> <ul id="toc-Other_maps_of_diagrams-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simply_laced" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Simply_laced"> <div class="vector-toc-text"> 9 Simply laced </div> </a> <ul id="toc-Simply_laced-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Satake_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Satake_diagrams"> <div class="vector-toc-text"> 10 Satake diagrams </div> </a> <ul id="toc-Satake_diagrams-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> 11 History </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conventions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Conventions"> <div class="vector-toc-text"> 12 Conventions </div> </a> <ul id="toc-Conventions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rank_2_Dynkin_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Rank_2_Dynkin_diagrams"> <div class="vector-toc-text"> 13 Rank 2 Dynkin diagrams </div> </a> <ul id="toc-Rank_2_Dynkin_diagrams-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Finite_Dynkin_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Finite_Dynkin_diagrams"> <div class="vector-toc-text"> 14 Finite Dynkin diagrams </div> </a> <ul id="toc-Finite_Dynkin_diagrams-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Affine_Dynkin_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Affine_Dynkin_diagrams"> <div class="vector-toc-text"> 15 Affine Dynkin diagrams </div> </a> <ul id="toc-Affine_Dynkin_diagrams-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hyperbolic_and_higher_Dynkin_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a 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16.2 Noncompact (over-extended) forms </div> </a> <ul id="toc-Noncompact_(over-extended)_forms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-238_Hyperbolic_groups_(compact_and_noncompact)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#238_Hyperbolic_groups_(compact_and_noncompact)"> <div class="vector-toc-text"> 16.3 238 Hyperbolic groups (compact and noncompact) </div> </a> <ul id="toc-238_Hyperbolic_groups_(compact_and_noncompact)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Very-extended" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Very-extended"> <div class="vector-toc-text"> 16.4 Very-extended </div> </a> <ul id="toc-Very-extended-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 17 See also </div> </a> <ul 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도표" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Diagramma_di_Dynkin" title="Diagramma di Dynkin – Italian" lang="it" hreflang="it" data-title="Diagramma di Dynkin" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%87%E3%82%A3%E3%83%B3%E3%82%AD%E3%83%B3%E5%9B%B3%E5%BD%A2" title="ディンキン図形 – Japanese" lang="ja" hreflang="ja" data-title="ディンキン図形" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Diagrama_de_Dynkin" title="Diagrama de Dynkin – Portuguese" lang="pt" hreflang="pt" data-title="Diagrama de Dynkin" 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href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="/wiki/Lie_group" title="Lie group">Lie groups</a> and <a href="/wiki/Lie_algebra" title="Lie algebra">Lie algebras</a></th></tr><tr><td class="sidebar-image skin-invert-image" style="padding-bottom:0.9em;"><a href="/wiki/File:E8Petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/250px-E8Petrie.svg.png" decoding="async" width="180" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/330px-E8Petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/500px-E8Petrie.svg.png 2x" data-file-width="2852" data-file-height="2863" /></a></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Classical_group" title="Classical group">Classical groups</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/General_linear_group" title="General linear group">General linear</a> GL(n)</li> <li><a href="/wiki/Special_linear_group" title="Special linear group">Special linear</a> SL(n)</li> <li><a href="/wiki/Orthogonal_group" title="Orthogonal group">Orthogonal</a> O(n)</li> <li><a href="/wiki/Special_orthogonal_group" class="mw-redirect" title="Special orthogonal group">Special orthogonal</a> SO(n)</li> <li><a href="/wiki/Unitary_group" title="Unitary group">Unitary</a> U(n)</li> <li><a href="/wiki/Special_unitary_group" title="Special unitary group">Special unitary</a> SU(n)</li> <li><a href="/wiki/Symplectic_group" title="Symplectic group">Symplectic</a> Sp(n)</li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Simple_Lie_group" title="Simple Lie group">Simple Lie groups</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks hlist" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="font-weight:normal; font-style:italic;"> Classical</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Simple_Lie_group#A_series" title="Simple Lie group">An</a></li> <li><a href="/wiki/Simple_Lie_group#B_series" title="Simple Lie group">Bn</a></li> <li><a href="/wiki/Simple_Lie_group#C_series" title="Simple Lie group">Cn</a></li> <li><a href="/wiki/Simple_Lie_group#D_series" title="Simple Lie group">Dn</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal; font-style:italic;"> Exceptional</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/G2_(mathematics)" title="G2 (mathematics)">G2</a></li> <li><a href="/wiki/F4_(mathematics)" title="F4 (mathematics)">F4</a></li> <li><a href="/wiki/E6_(mathematics)" title="E6 (mathematics)">E6</a></li> <li><a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E7</a></li> <li><a href="/wiki/E8_(mathematics)" title="E8 (mathematics)">E8</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Table_of_Lie_groups" title="Table of Lie groups">Other Lie groups</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Circle_group" title="Circle group">Circle</a></li> <li><a href="/wiki/Lorentz_group" title="Lorentz group">Lorentz</a></li> <li><a href="/wiki/Poincar%C3%A9_group" title="Poincaré group">Poincaré</a></li> <li><a href="/wiki/Conformal_group" title="Conformal group">Conformal group</a></li> <li><a href="/wiki/Diffeomorphism" title="Diffeomorphism">Diffeomorphism</a></li> <li><a href="/wiki/Loop_group" title="Loop group">Loop</a></li> <li><a href="/wiki/Euclidean_group" title="Euclidean group">Euclidean</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Lie_algebra" title="Lie algebra">Lie algebras</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Lie_group%E2%80%93Lie_algebra_correspondence" title="Lie group–Lie algebra correspondence">Lie group–Lie algebra correspondence</a></li> <li><a href="/wiki/Exponential_map_(Lie_theory)" title="Exponential map (Lie theory)">Exponential map</a></li> <li><a href="/wiki/Adjoint_representation" title="Adjoint representation">Adjoint representation</a></li> <li><div class="hlist"><ul><li><a href="/wiki/Killing_form" title="Killing form">Killing form</a></li><li><a href="/wiki/Index_of_a_Lie_algebra" title="Index of a Lie algebra">Index</a></li></ul></div></li> <li><a href="/wiki/Simple_Lie_algebra" title="Simple Lie algebra">Simple Lie algebra</a></li> <li><a href="/wiki/Loop_algebra" title="Loop algebra">Loop algebra</a></li> <li><a href="/wiki/Affine_Lie_algebra" title="Affine Lie algebra">Affine Lie algebra</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Semisimple_Lie_algebra" title="Semisimple Lie algebra">Semisimple Lie algebra</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a class="mw-selflink selflink">Dynkin diagrams</a></li> <li><a href="/wiki/Cartan_subalgebra" title="Cartan subalgebra">Cartan subalgebra</a></li> <li><div class="hlist"><ul><li><a href="/wiki/Root_system" title="Root system">Root system</a></li><li><a href="/wiki/Weyl_group" title="Weyl group">Weyl group</a></li></ul></div></li> <li><div class="hlist"><ul><li><a href="/wiki/Real_form_(Lie_theory)" title="Real form (Lie theory)">Real form</a></li><li><a href="/wiki/Complexification_(Lie_group)" title="Complexification (Lie group)">Complexification</a></li></ul></div></li> <li><a href="/wiki/Split_Lie_algebra" title="Split Lie algebra">Split Lie algebra</a></li> <li><a href="/wiki/Compact_Lie_algebra" title="Compact Lie algebra">Compact Lie algebra</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Representation_theory" title="Representation theory">Representation theory</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Representation_of_a_Lie_group" title="Representation of a Lie group">Lie group representation</a></li> <li><a href="/wiki/Lie_algebra_representation" title="Lie algebra representation">Lie algebra representation</a></li> <li><a href="/wiki/Representation_theory_of_semisimple_Lie_algebras" title="Representation theory of semisimple Lie algebras">Representation theory of semisimple Lie algebras</a></li> <li><a href="/wiki/Representations_of_classical_Lie_groups" title="Representations of classical Lie groups">Representations of classical Lie groups</a></li> <li><a href="/wiki/Theorem_of_the_highest_weight" title="Theorem of the highest weight">Theorem of the highest weight</a></li> <li><a href="/wiki/Borel%E2%80%93Weil%E2%80%93Bott_theorem" title="Borel–Weil–Bott theorem">Borel–Weil–Bott theorem</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Lie groups in <a href="/wiki/Physics" title="Physics">physics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Particle_physics_and_representation_theory" title="Particle physics and representation theory">Particle physics and representation theory</a></li> <li><a href="/wiki/Representation_theory_of_the_Lorentz_group" title="Representation theory of the Lorentz group">Lorentz group representations</a></li> <li><a href="/wiki/Representation_theory_of_the_Poincar%C3%A9_group" title="Representation theory of the Poincaré group">Poincaré group representations</a></li> <li><a href="/wiki/Representation_theory_of_the_Galilean_group" title="Representation theory of the Galilean group">Galilean group representations</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Sophus_Lie" title="Sophus Lie">Sophus Lie</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li><a href="/wiki/Wilhelm_Killing" title="Wilhelm Killing">Wilhelm Killing</a></li> <li><a href="/wiki/%C3%89lie_Cartan" title="Élie Cartan">Élie Cartan</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a></li> <li><a href="/wiki/Claude_Chevalley" title="Claude Chevalley">Claude Chevalley</a></li> <li><a href="/wiki/Harish-Chandra" title="Harish-Chandra">Harish-Chandra</a></li> <li><a href="/wiki/Armand_Borel" title="Armand Borel">Armand Borel</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below plainlist"> <ul><li><a href="/wiki/Glossary_of_Lie_groups_and_Lie_algebras" title="Glossary of Lie groups and Lie algebras">Glossary</a></li> <li><a href="/wiki/Table_of_Lie_groups" title="Table of Lie groups">Table of Lie groups</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Lie_groups" title="Template:Lie groups"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Lie_groups" title="Template talk:Lie groups"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Lie_groups" title="Special:EditPage/Template:Lie groups"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> In the <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> field of <a href="/wiki/Lie_theory" title="Lie theory">Lie theory</a>, a Dynkin diagram, named for <a href="/wiki/Eugene_Dynkin" title="Eugene Dynkin">Eugene Dynkin</a>, is a type of <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">graph</a> with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of <a href="/wiki/Semisimple_Lie_algebra" title="Semisimple Lie algebra">semisimple Lie algebras</a> over <a href="/wiki/Algebraically_closed_field" title="Algebraically closed field">algebraically closed fields</a>, in the classification of <a href="/wiki/Weyl_group" title="Weyl group">Weyl groups</a> and other <a href="/wiki/Finite_reflection_group" class="mw-redirect" title="Finite reflection group">finite reflection groups</a>, and in other contexts. Various properties of the Dynkin diagram (such as whether it contains multiple edges, or its symmetries) correspond to important features of the associated Lie algebra. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Finite_Dynkin_diagrams.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Finite_Dynkin_diagrams.svg/220px-Finite_Dynkin_diagrams.svg.png" decoding="async" width="220" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Finite_Dynkin_diagrams.svg/330px-Finite_Dynkin_diagrams.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Finite_Dynkin_diagrams.svg/440px-Finite_Dynkin_diagrams.svg.png 2x" data-file-width="860" data-file-height="300" /></a><figcaption>Finite Dynkin diagrams</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Affine_Dynkin_diagrams.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Affine_Dynkin_diagrams.png/220px-Affine_Dynkin_diagrams.png" decoding="async" width="220" height="84" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Affine_Dynkin_diagrams.png/330px-Affine_Dynkin_diagrams.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Affine_Dynkin_diagrams.png/440px-Affine_Dynkin_diagrams.png 2x" data-file-width="693" data-file-height="265" /></a><figcaption>Affine (extended) Dynkin diagrams</figcaption></figure> The term "Dynkin diagram" can be ambiguous. In some cases, Dynkin diagrams are assumed to be <a href="/wiki/Directed_graph" title="Directed graph">directed</a>, in which case they correspond to <a href="/wiki/Root_system" title="Root system">root systems</a> and semi-simple Lie algebras, while in other cases they are assumed to be <a href="/wiki/Undirected_graph" class="mw-redirect" title="Undirected graph">undirected</a>, in which case they correspond to Weyl groups. In this article, "Dynkin diagram" means directed Dynkin diagram, and undirected Dynkin diagrams will be explicitly so named. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Classification_of_semisimple_Lie_algebras">Classification of semisimple Lie algebras</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=1" title="Edit section: Classification of semisimple Lie algebras">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Semisimple_Lie_algebra#Classification" title="Semisimple Lie algebra">Semisimple Lie algebra § Classification</a></div> The fundamental interest in Dynkin diagrams is that they classify <a href="/wiki/Semisimple_Lie_algebra" title="Semisimple Lie algebra">semisimple Lie algebras</a> over <a href="/wiki/Algebraically_closed_field" title="Algebraically closed field">algebraically closed fields</a>. One classifies such Lie algebras via their <a href="/wiki/Root_system" title="Root system">root system</a>, which can be represented by a Dynkin diagram. One then classifies Dynkin diagrams according to the constraints they must satisfy, as described below. Dropping the direction on the graph edges corresponds to replacing a root system by the <a href="/wiki/Finite_reflection_group" class="mw-redirect" title="Finite reflection group">finite reflection group</a> it generates, the so-called <a href="/wiki/Weyl_group" title="Weyl group">Weyl group</a>, and thus undirected Dynkin diagrams classify Weyl groups. They have the following correspondence for the Lie algebras associated to classical groups over the complex numbers: <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/730f6906700685b6d52f3958b1c2ae659d2d97d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.962ex; height:2.509ex;" alt="{\displaystyle A_{n}}" />: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {sl}}_{n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">l</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {sl}}_{n+1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1639a3cc3b1f5e57f7550a8198a89d3dc2a4e2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:5.041ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {sl}}_{n+1}}" />, the <a href="/wiki/Special_linear_Lie_algebra" title="Special linear Lie algebra">special linear Lie algebra</a>.</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f568bf6d34e97b9fdda0dc7e276d6c4501d2045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.982ex; height:2.509ex;" alt="{\displaystyle B_{n}}" />: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {so}}_{2n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {so}}_{2n+1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e4b690129a4c1d766e0c0d61785f3f5265775f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:6.349ex; height:2.009ex;" alt="{\displaystyle {\mathfrak {so}}_{2n+1}}" />, the odd-dimensional <a href="/wiki/Special_orthogonal_Lie_algebra" class="mw-redirect" title="Special orthogonal Lie algebra">special orthogonal Lie algebra</a>.</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0301812adb392070d834ca2df4ed97f1cf132f33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.88ex; height:2.509ex;" alt="{\displaystyle C_{n}}" />: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {sp}}_{2n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">p</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {sp}}_{2n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e79984b916df6d4ade207946515585d558a7c6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.041ex; width:4.274ex; height:2.343ex;" alt="{\displaystyle {\mathfrak {sp}}_{2n}}" />, the <a href="/wiki/Symplectic_Lie_algebra" class="mw-redirect" title="Symplectic Lie algebra">symplectic Lie algebra</a>.</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe03857347bf517e7fbda4085b0dafd6018cf18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.143ex; height:2.509ex;" alt="{\displaystyle D_{n}}" />: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {so}}_{2n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {so}}_{2n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af8fee7591b5719475675143e59f60737207eda4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:4.248ex; height:2.009ex;" alt="{\displaystyle {\mathfrak {so}}_{2n}}" />, the even-dimensional <a href="/wiki/Special_orthogonal_Lie_algebra" class="mw-redirect" title="Special orthogonal Lie algebra">special orthogonal Lie algebra</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee74e1cc07e7041edf0fcbd4481f5cd32ad17b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n>1}" />).</li></ul> For the exceptional groups, the names for the Lie algebra and the associated Dynkin diagram coincide. <div class="mw-heading mw-heading2"><h2 id="Related_classifications">Related classifications</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=2" title="Edit section: Related classifications">edit</a>]</div> Dynkin diagrams can be interpreted as classifying many distinct, related objects, and the notation "An, Bn, ..." is used to refer to all such interpretations, depending on context; this ambiguity can be confusing. The central classification is that a simple Lie algebra has a root system, to which is associated an (oriented) Dynkin diagram; all three of these may be referred to as Bn, for instance. The unoriented Dynkin diagram is a form of <a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a>, and corresponds to the Weyl group, which is the <a href="/wiki/Finite_reflection_group" class="mw-redirect" title="Finite reflection group">finite reflection group</a> associated to the root system. Thus Bn may refer to the unoriented diagram (a special kind of Coxeter diagram), the Weyl group (a concrete reflection group), or the abstract Coxeter group. Although the Weyl group is abstractly isomorphic to the Coxeter group, a specific isomorphism depends on an ordered choice of simple roots. Likewise, while Dynkin diagram notation is standardized, Coxeter diagram and group notation is varied and sometimes agrees with Dynkin diagram notation and sometimes does not.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Lastly, sometimes associated objects are referred to by the same notation, though this cannot always be done regularly. Examples include: <ul><li>The <a href="/wiki/Root_lattice" class="mw-redirect" title="Root lattice">root lattice</a> generated by the root system, as in the <a href="/wiki/E8_lattice" title="E8 lattice">E8 lattice</a>. This is naturally defined, but not one-to-one – for example, A2 and G2 both generate the <a href="/wiki/Hexagonal_lattice" title="Hexagonal lattice">hexagonal lattice</a>.</li> <li>An associated polytope – for example <a href="/wiki/Gosset_4_21_polytope" class="mw-redirect" title="Gosset 4 21 polytope">Gosset 421 polytope</a> may be referred to as "the E8 polytope", as its vertices are derived from the E8 root system and it has the E8 Coxeter group as symmetry group.</li> <li>An associated quadratic form or manifold – for example, the <a href="/wiki/E8_manifold" title="E8 manifold">E8 manifold</a> has <a href="/wiki/Intersection_form_(4-manifold)" class="mw-redirect" title="Intersection form (4-manifold)">intersection form</a> given by the E8 lattice.</li></ul> These latter notations are mostly used for objects associated with exceptional diagrams – objects associated to the regular diagrams (A, B, C, D) instead have traditional names. The index (the n) equals to the number of nodes in the diagram, the number of simple roots in a basis, the dimension of the root lattice and span of the root system, the number of generators of the Coxeter group, and the rank of the Lie algebra. However, n does not equal the dimension of the defining module (a <a href="/wiki/Fundamental_representation" title="Fundamental representation">fundamental representation</a>) of the Lie algebra – the index on the Dynkin diagram should not be confused with the index on the Lie algebra. For example, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/060d6a804a294151c5d464fb355af272c597b409" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle B_{4}}" /> corresponds to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {so}}_{2\cdot 4+1}={\mathfrak {so}}_{9},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>⋅</mo> <mn>4</mn> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {so}}_{2\cdot 4+1}={\mathfrak {so}}_{9},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eb6fd19bf3bac6d38550ec06174248bacb3159f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:13.608ex; height:2.009ex;" alt="{\displaystyle {\mathfrak {so}}_{2\cdot 4+1}={\mathfrak {so}}_{9},}" /> which naturally acts on 9-dimensional space, but has rank 4 as a Lie algebra. The <a href="#Simply_laced">simply laced</a> Dynkin diagrams, those with no multiple edges (A, D, E) classify many further mathematical objects; see discussion at <a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a>. <div class="mw-heading mw-heading3"><h3 id="Example:_A2">Example: A2</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=3" title="Edit section: Example: A2">edit</a>]</div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Root_system_A2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/220px-Root_system_A2.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/330px-Root_system_A2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/440px-Root_system_A2.svg.png 2x" data-file-width="600" data-file-height="600" /></a><figcaption>The <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ec73b8bc9abc3efb934f5a6ec2803713771f4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{2}}" /> root system</figcaption></figure> For example, the symbol <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ec73b8bc9abc3efb934f5a6ec2803713771f4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{2}}" /> may refer to: <ul><li>The Dynkin diagram with 2 connected nodes, <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" />, which may also be interpreted as a <a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagram</a>.</li> <li>The <a href="/wiki/Root_system" title="Root system">root system</a> with 2 simple roots at a <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi /3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi /3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e36a1526c55cd78034e9cc1e71f5c5f14f25d803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.819ex; height:2.843ex;" alt="{\displaystyle 2\pi /3}" /> (120 degree) angle.</li> <li>The Lie algebra <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {sl}}_{2+1}={\mathfrak {sl}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">l</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">l</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {sl}}_{2+1}={\mathfrak {sl}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51ec7650ae61098cc2183f8cfe51438be50dbfcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:10.711ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {sl}}_{2+1}={\mathfrak {sl}}_{3}}" /> of <a href="/wiki/Rank_(Lie_algebra)" class="mw-redirect" title="Rank (Lie algebra)">rank</a> 2.</li> <li>The <a href="/wiki/Weyl_group" title="Weyl group">Weyl group</a> of symmetries of the roots (reflections in the hyperplane orthogonal to the roots), isomorphic to the <a href="/wiki/Symmetric_group" title="Symmetric group">symmetric group</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70e15f3e200aaa247f69c43110cc5a09ecc91b89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{3}}" /> (of order 6).</li> <li>The abstract <a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter group</a>, presented by generators and relations, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle r_{1},r_{2}\mid (r_{1})^{2}=(r_{2})^{2}=(r_{i}r_{j})^{3}=1\right\rangle .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>∣</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mrow> <mo>⟩</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle r_{1},r_{2}\mid (r_{1})^{2}=(r_{2})^{2}=(r_{i}r_{j})^{3}=1\right\rangle .}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/810182f2d732786ad65886a713b7f3eb695d0e99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:37.467ex; height:3.343ex;" alt="{\displaystyle \left\langle r_{1},r_{2}\mid (r_{1})^{2}=(r_{2})^{2}=(r_{i}r_{j})^{3}=1\right\rangle .}" /></li></ul> <div class="mw-heading mw-heading2"><h2 id="Construction_from_root_systems">Construction from root systems</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=4" title="Edit section: Construction from root systems">edit</a>]</div> Consider a <a href="/wiki/Root_system" title="Root system">root system</a>, assumed to be reduced and integral (or "crystallographic"). In many applications, this root system will arise from a <a href="/wiki/Semisimple_Lie_algebra" title="Semisimple Lie algebra">semisimple Lie algebra</a>. Let <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }" /> be a set of <a href="/wiki/Root_system#Positive_roots_and_simple_roots" title="Root system">positive simple roots</a>. We then construct a diagram from <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }" /> as follows.<a href="#cite_note-1">[1]</a> Form a graph with one vertex for each element of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }" />. Then insert edges between each pair of vertices according to the following recipe. If the roots corresponding to the two vertices are orthogonal, there is no edge between the vertices. If the angle between the two roots is 120 degrees, we put one edge between the vertices. If the angle is 135 degrees, we put two edges, and if the angle is 150 degrees, we put three edges. (These four cases exhaust all possible angles between pairs of positive simple roots.<a href="#cite_note-2">[2]</a>) Finally, if there are any edges between a given pair of vertices, we decorate them with an arrow pointing from the vertex corresponding to the longer root to the vertex corresponding to the shorter one. (The arrow is omitted if the roots have the same length.) Thinking of the arrow as a "greater than" sign makes it clear which way the arrow should go. Dynkin diagrams lead to a <a href="/wiki/Root_system#Classification_of_root_systems_by_Dynkin_diagrams" title="Root system">classification</a> of root systems. The angles and length ratios between roots are <a href="/wiki/Root_system#Elementary_consequences_of_the_root_system_axioms" title="Root system">related</a>.<a href="#cite_note-3">[3]</a> Thus, the edges for non-orthogonal roots may alternatively be described as one edge for a length ratio of 1, two edges for a length ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}" />, and three edges for a length ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {3}}}" />. (There are no edges when the roots are orthogonal, regardless of the length ratio.) In the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ec73b8bc9abc3efb934f5a6ec2803713771f4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{2}}" /> root system, shown at right, the roots labeled <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /> form a base. Since these two roots are at angle of 120 degrees (with a length ratio of 1), the Dynkin diagram consists of two vertices connected by a single edge: <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" />. <div class="mw-heading mw-heading2"><h2 id="Constraints">Constraints</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=5" title="Edit section: Constraints">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 1.5x" data-file-width="44" data-file-height="31" /></a></td><td class="mbox-text"><div class="mbox-text-span">This section needs expansion. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Dynkin_diagram&action=edit&section=">adding to it</a>. (December 2009)</div></td></tr></tbody></table> Dynkin diagrams must satisfy certain constraints; these are essentially those satisfied by finite <a href="/wiki/Coxeter%E2%80%93Dynkin_diagram" title="Coxeter–Dynkin diagram">Coxeter–Dynkin diagrams</a>, together with an additional crystallographic constraint. <div class="mw-heading mw-heading2"><h2 id="Connection_with_Coxeter_diagrams">Connection with Coxeter diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=6" title="Edit section: Connection with Coxeter diagrams">edit</a>]</div> Dynkin diagrams are closely related to <a href="/wiki/Coxeter%E2%80%93Dynkin_diagram" title="Coxeter–Dynkin diagram">Coxeter diagrams</a> of finite <a href="/wiki/Coxeter_group" title="Coxeter group">Coxeter groups</a>, and the terminology is often conflated.<a href="#cite_note-4">[note 1]</a> Dynkin diagrams differ from Coxeter diagrams of finite groups in two important respects: <dl><dt>Partly directed</dt> <dd>Dynkin diagrams are partly <a href="/wiki/Directed_graph" title="Directed graph">directed</a> – any multiple edge (in Coxeter terms, labeled with "4" or above) has a direction (an arrow pointing from one node to the other); thus Dynkin diagrams have more data than the underlying Coxeter diagram (undirected graph).</dd> <dd>At the level of root systems the direction corresponds to pointing towards the shorter vector; edges labeled "3" have no direction because the corresponding vectors must have equal length. (Caution: Some authors reverse this convention, with the arrow pointing towards the longer vector.)</dd> <dt>Crystallographic restriction</dt> <dd>Dynkin diagrams must satisfy an additional restriction, namely that the only allowable edge labels are 2, 3, 4, and 6, a restriction not shared by Coxeter diagrams, so not every Coxeter diagram of a finite group comes from a Dynkin diagram.</dd> <dd>At the level of root systems this corresponds to the <a href="/wiki/Crystallographic_restriction_theorem" title="Crystallographic restriction theorem">crystallographic restriction theorem</a>, as the roots form a lattice.</dd></dl> A further difference, which is only stylistic, is that Dynkin diagrams are conventionally drawn with double or triple edges between nodes (for p = 4, 6), rather than an edge labeled with "p". The term "Dynkin diagram" at times refers to the directed graph, at times to the undirected graph. For precision, in this article "Dynkin diagram" will mean directed, and the underlying undirected graph will be called an "undirected Dynkin diagram". Then Dynkin diagrams and Coxeter diagrams may be related as follows: <table class="wikitable" border="1"> <tbody><tr> <th></th> <th>crystallographic</th> <th>point group </th></tr> <tr> <th>directed </th> <td>Dynkin diagrams </td></tr> <tr> <th>undirected </th> <td>undirected Dynkin diagrams </td> <td>Coxeter diagrams of finite groups </td></tr></tbody></table> By this is meant that Coxeter diagrams of finite groups correspond to <a href="/wiki/Point_group" title="Point group">point groups</a> generated by reflections, while Dynkin diagrams must satisfy an additional restriction corresponding to the <a href="/wiki/Crystallographic_restriction_theorem" title="Crystallographic restriction theorem">crystallographic restriction theorem</a>, and that Coxeter diagrams are undirected, while Dynkin diagrams are (partly) directed. The corresponding mathematical objects classified by the diagrams are: <table class="wikitable" border="1"> <tbody><tr> <th></th> <th>crystallographic</th> <th>point group </th></tr> <tr> <th>directed </th> <td><a href="/wiki/Root_system" title="Root system">root systems</a> </td></tr> <tr> <th>undirected </th> <td><a href="/wiki/Weyl_group" title="Weyl group">Weyl groups</a> </td> <td><a href="/wiki/Finite_Coxeter_group" class="mw-redirect" title="Finite Coxeter group">finite Coxeter groups</a> </td></tr></tbody></table> The blank in the upper right, corresponding to directed graphs with underlying undirected graph any Coxeter diagram (of a finite group), can be defined formally, but is little-discussed, and does not appear to admit a simple interpretation in terms of mathematical objects of interest. There are natural maps down – from Dynkin diagrams to undirected Dynkin diagrams; respectively, from root systems to the associated Weyl groups – and right – from undirected Dynkin diagrams to Coxeter diagrams; respectively from Weyl groups to finite Coxeter groups. The down map is onto (by definition) but not one-to-one, as the Bn and Cn diagrams map to the same undirected diagram, with the resulting Coxeter diagram and Weyl group thus sometimes denoted BCn. The right map is simply an inclusion – undirected Dynkin diagrams are special cases of Coxeter diagrams, and Weyl groups are special cases of finite Coxeter groups – and is not onto, as not every Coxeter diagram is an undirected Dynkin diagram (the missed diagrams being H3, H4 and I2(p) for p = 5 p ≥ 7), and correspondingly not every finite Coxeter group is a Weyl group. <div class="mw-heading mw-heading2"><h2 id="Isomorphisms">Isomorphisms</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=7" title="Edit section: Isomorphisms">edit</a>]</div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_Diagram_Isomorphisms.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Dynkin_Diagram_Isomorphisms.svg/170px-Dynkin_Diagram_Isomorphisms.svg.png" decoding="async" width="170" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Dynkin_Diagram_Isomorphisms.svg/255px-Dynkin_Diagram_Isomorphisms.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Dynkin_Diagram_Isomorphisms.svg/340px-Dynkin_Diagram_Isomorphisms.svg.png 2x" data-file-width="375" data-file-height="450" /></a><figcaption>The <a href="/wiki/Exceptional_isomorphism" title="Exceptional isomorphism">exceptional isomorphisms</a> of connected Dynkin diagrams.</figcaption></figure> Dynkin diagrams are conventionally numbered so that the list is non-redundant: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ce9ce38d06f6bf5a3fe063118c09c2b6202bfe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 1}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fae867c6cf39dce3d32fc508abf43810a970743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.608ex; height:2.509ex;" alt="{\displaystyle A_{n},}" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bf67f9d06ca3af619657f8d20ee1322da77174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 2}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57b99b300d1dca17f7f73aaa6e8509ea486c57c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.629ex; height:2.509ex;" alt="{\displaystyle B_{n},}" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73136e4a27fe39c123d16a7808e76d3162ce42bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 3}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e51eedd4515184daee3f8ad35f3762b442306f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.527ex; height:2.509ex;" alt="{\displaystyle C_{n},}" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 4}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25010fec4b0f68f1b46f49d14917d962acca0b16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 4}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f791ccfe467d310fef894c66d25763afacfb438e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.79ex; height:2.509ex;" alt="{\displaystyle D_{n},}" /> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad6b82f2a00af6c9efd4c16d4e99329605645c0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.934ex; height:2.509ex;" alt="{\displaystyle E_{n}}" /> starting at <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=6.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>6.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=6.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5abbaa1ee6ec8fa2b8473dbe2e3f391aa2b93f32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.302ex; height:2.176ex;" alt="{\displaystyle n=6.}" /> The families can however be defined for lower n, yielding <a href="/wiki/Exceptional_isomorphism" title="Exceptional isomorphism">exceptional isomorphisms</a> of diagrams, and corresponding exceptional isomorphisms of Lie algebras and associated Lie groups. Trivially, one can start the families at <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26819344e55f5e671c76c07c18eb4291fcec85ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=0}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=1,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dba4db03e5186e479ecd9611484b8657140a7ff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.302ex; height:2.509ex;" alt="{\displaystyle n=1,}" /> which are all then isomorphic as there is a unique empty diagram and a unique 1-node diagram. The other isomorphisms of connected Dynkin diagrams are: <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}\cong B_{1}\cong C_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}\cong B_{1}\cong C_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34385927fe89603084d7ab3725c52f05c83a2c5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.529ex; height:2.509ex;" alt="{\displaystyle A_{1}\cong B_{1}\cong C_{1}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{2}\cong C_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{2}\cong C_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/067f9d1c08cc1f9ec999ce9960a62cb5ff85014b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.633ex; height:2.509ex;" alt="{\displaystyle B_{2}\cong C_{2}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{2}\cong A_{1}\times A_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{2}\cong A_{1}\times A_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4c11c64859da2459a79d0b18171bfc8dbb4697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.512ex; height:2.509ex;" alt="{\displaystyle D_{2}\cong A_{1}\times A_{1}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{3}\cong A_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{3}\cong A_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5959ebf014561539609bb8551e70b08ca9812222" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.509ex;" alt="{\displaystyle D_{3}\cong A_{3}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{3}\cong A_{1}\times A_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{3}\cong A_{1}\times A_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78ef8dd99dc6dfebb4c4db586597c69c5b3f64f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.303ex; height:2.509ex;" alt="{\displaystyle E_{3}\cong A_{1}\times A_{2}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{4}\cong A_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{4}\cong A_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6640910e134a698d509a05406f43f42ef27ea2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.665ex; height:2.509ex;" alt="{\displaystyle E_{4}\cong A_{4}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{5}\cong D_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mo>≅</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{5}\cong D_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1469caa9228a2c979650077ae04f7ee9facb2bec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.846ex; height:2.509ex;" alt="{\displaystyle E_{5}\cong D_{5}}" /></li></ul> These isomorphisms correspond to isomorphism of simple and semisimple Lie algebras, which also correspond to certain isomorphisms of Lie group forms of these. They also add context to the <a href="/wiki/En_(Lie_algebra)" title="En (Lie algebra)">En family</a>.<a href="#cite_note-5">[4]</a> <div class="mw-heading mw-heading2"><h2 id="Automorphisms">Automorphisms</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=8" title="Edit section: Automorphisms">edit</a>]</div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_diagram_D4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/59/Dynkin_diagram_D4.png" decoding="async" width="133" height="148" class="mw-file-element" data-file-width="133" data-file-height="148" /></a><figcaption>The most symmetric Dynkin diagram is D4, which gives rise to <a href="/wiki/Triality" title="Triality">triality</a>.</figcaption></figure> In addition to isomorphism between different diagrams, some diagrams also have self-isomorphisms or "<a href="/wiki/Automorphism" title="Automorphism">automorphisms</a>". Diagram automorphisms correspond to <a href="/wiki/Outer_automorphism" class="mw-redirect" title="Outer automorphism">outer automorphisms</a> of the Lie algebra, meaning that the outer automorphism group Out = Aut/Inn equals the group of diagram automorphisms.<a href="#cite_note-6">[5]</a><a href="#cite_note-overout-7">[6]</a><a href="#cite_note-8">[7]</a> The diagrams that have non-trivial automorphisms are An (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee74e1cc07e7041edf0fcbd4481f5cd32ad17b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n>1}" />), Dn (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee74e1cc07e7041edf0fcbd4481f5cd32ad17b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n>1}" />), and E6. In all these cases except for D4, there is a single non-trivial automorphism (Out = C2, the cyclic group of order 2), while for D4, the automorphism group is the <a href="/wiki/Symmetric_group" title="Symmetric group">symmetric group</a> on three letters (S3, order 6) – this phenomenon is known as "<a href="/wiki/Triality" title="Triality">triality</a>". It happens that all these diagram automorphisms can be realized as Euclidean symmetries of how the diagrams are conventionally drawn in the plane, but this is just an artifact of how they are drawn, and not intrinsic structure. <figure class="skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_diagram_An_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Dynkin_diagram_An_2.png/250px-Dynkin_diagram_An_2.png" decoding="async" width="160" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Dynkin_diagram_An_2.png/320px-Dynkin_diagram_An_2.png 2x" data-file-width="329" data-file-height="32" /></a><figcaption>An.</figcaption></figure> For An, the diagram automorphism is reversing the diagram, which is a line. The nodes of the diagram index the <a href="/wiki/Fundamental_weight" class="mw-redirect" title="Fundamental weight">fundamental weights</a>, which (for An−1) are <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigwedge ^{i}C^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mover> <mo>⋀</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </mover> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigwedge ^{i}C^{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3da6ba5cd7a1c29cfa82ff9c00c5d3aa5cdca2d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:5.985ex; height:5.509ex;" alt="{\displaystyle \bigwedge ^{i}C^{n}}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=1,\dots ,n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=1,\dots ,n}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3f269b2f3b2f87fec0168426652a5ea80b56112" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.636ex; height:2.509ex;" alt="{\displaystyle i=1,\dots ,n}" />, and the diagram automorphism corresponds to the duality <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigwedge ^{i}C^{n}\mapsto \bigwedge ^{n-i}C^{n}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mover> <mo>⋀</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </mover> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">↦</mo> <mover> <mo>⋀</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>i</mi> </mrow> </mover> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigwedge ^{i}C^{n}\mapsto \bigwedge ^{n-i}C^{n}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/863dd86ac47c0e26406cee3dc05e425f0557cdce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:16.481ex; height:5.509ex;" alt="{\displaystyle \bigwedge ^{i}C^{n}\mapsto \bigwedge ^{n-i}C^{n}.}" /> Realized as the Lie algebra <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {sl}}_{n+1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">l</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {sl}}_{n+1},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9d2bb9027314502e00630af62f3ce462ef882fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:5.688ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {sl}}_{n+1},}" /> the outer automorphism can be expressed as negative transpose, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\mapsto -T^{\mathrm {T} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo stretchy="false">↦</mo> <mo>−</mo> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\mapsto -T^{\mathrm {T} }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc527f8c7378962fd13a681eac484bdb691fa60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.197ex; height:2.843ex;" alt="{\displaystyle T\mapsto -T^{\mathrm {T} }}" />, which is how the dual representation acts.<a href="#cite_note-overout-7">[6]</a> <figure class="skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_diagram_Dn_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Dynkin_diagram_Dn_2.png/250px-Dynkin_diagram_Dn_2.png" decoding="async" width="160" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Dynkin_diagram_Dn_2.png/320px-Dynkin_diagram_Dn_2.png 2x" data-file-width="329" data-file-height="148" /></a><figcaption>Dn.</figcaption></figure> For Dn, the diagram automorphism is switching the two nodes at the end of the Y, and corresponds to switching the two <a href="/wiki/Chirality_(mathematics)" title="Chirality (mathematics)">chiral</a> <a href="/wiki/Spin_representation" title="Spin representation">spin representations</a>. Realized as the Lie algebra <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {so}}_{2n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">o</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {so}}_{2n},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/731d8c2033988e8f6d1e9f29e1efc67d9f847c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.041ex; width:4.895ex; height:2.009ex;" alt="{\displaystyle {\mathfrak {so}}_{2n},}" /> the outer automorphism can be expressed as conjugation by a matrix in O(2n) with determinant −1. When n = 3, one has <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {D} _{3}\cong \mathrm {A} _{3},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>≅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {D} _{3}\cong \mathrm {A} _{3},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2c94838e287fadbb4fd029c86db294d26fcc5e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.373ex; height:2.509ex;" alt="{\displaystyle \mathrm {D} _{3}\cong \mathrm {A} _{3},}" /> so their automorphisms agree, while <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {D} _{2}\cong \mathrm {A} _{1}\times \mathrm {A} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {D} _{2}\cong \mathrm {A} _{1}\times \mathrm {A} _{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d27aacd4c0183e20968f8d7e87c56f73af0ddc77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.363ex; height:2.509ex;" alt="{\displaystyle \mathrm {D} _{2}\cong \mathrm {A} _{1}\times \mathrm {A} _{1}}" /> is disconnected, and the automorphism corresponds to switching the two nodes. For D4, the <a href="/wiki/Fundamental_representation" title="Fundamental representation">fundamental representation</a> is isomorphic to the two spin representations, and the resulting <a href="/wiki/Symmetric_group" title="Symmetric group">symmetric group</a> on three letter (S3, or alternatively the <a href="/wiki/Dihedral_group" title="Dihedral group">dihedral group</a> of order 6, Dih3) corresponds both to automorphisms of the Lie algebra and automorphisms of the diagram. <figure class="skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_diagram_E6_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Dynkin_diagram_E6_2.png/250px-Dynkin_diagram_E6_2.png" decoding="async" width="160" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/6f/Dynkin_diagram_E6_2.png 2x" data-file-width="273" data-file-height="91" /></a><figcaption>E6.</figcaption></figure> The automorphism group of E6 corresponds to reversing the diagram, and can be expressed using <a href="/wiki/Jordan_algebra" title="Jordan algebra">Jordan algebras</a>.<a href="#cite_note-overout-7">[6]</a><a href="#cite_note-9">[8]</a> Disconnected diagrams, which correspond to semisimple Lie algebras, may have automorphisms from exchanging components of the diagram. <figure class="skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Dynkin_diagram_F4_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Dynkin_diagram_F4_2.png/160px-Dynkin_diagram_F4_2.png" decoding="async" width="160" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/66/Dynkin_diagram_F4_2.png 1.5x" data-file-width="215" data-file-height="32" /></a><figcaption>In characteristic 2, the arrow on F4 can be ignored, yielding an additional diagram automorphism and corresponding <a href="/wiki/Suzuki%E2%80%93Ree_group" class="mw-redirect" title="Suzuki–Ree group">Suzuki–Ree groups</a>.</figcaption></figure> In <a href="/wiki/Positive_characteristic" class="mw-redirect" title="Positive characteristic">positive characteristic</a> there are additional "diagram automorphisms" – roughly speaking, in characteristic p one is sometimes allowed to ignore the arrow on bonds of multiplicity p in the Dynkin diagram when taking diagram automorphisms. Thus in characteristic 2 there is an order 2 automorphism of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {B} _{2}\cong \mathrm {C} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {B} _{2}\cong \mathrm {C} _{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/643d42fc1504cd7d38698e246819df3ee9d7437f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.531ex; height:2.509ex;" alt="{\displaystyle \mathrm {B} _{2}\cong \mathrm {C} _{2}}" /> and of F4, while in characteristic 3 there is an order 2 automorphism of G2. But doesn't apply in all circumstances: for example, such automorphisms need not arise as automorphisms of the corresponding algebraic group, but rather on the level of points valued in a finite field. <div class="mw-heading mw-heading3"><h3 id="Construction_of_Lie_groups_via_diagram_automorphisms">Construction of Lie groups via diagram automorphisms</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=9" title="Edit section: Construction of Lie groups via diagram automorphisms">edit</a>]</div> Diagram automorphisms in turn yield additional <a href="/wiki/Lie_group" title="Lie group">Lie groups</a> and <a href="/wiki/Groups_of_Lie_type" class="mw-redirect" title="Groups of Lie type">groups of Lie type</a>, which are of central importance in the classification of finite simple groups. The <a href="/wiki/Chevalley_group" class="mw-redirect" title="Chevalley group">Chevalley group</a> construction of Lie groups in terms of their Dynkin diagram does not yield some of the classical groups, namely the unitary groups and the non-<a href="/wiki/Split_orthogonal_group" class="mw-redirect" title="Split orthogonal group">split orthogonal groups</a>. The <a href="/wiki/Steinberg_group_(Lie_theory)" class="mw-redirect" title="Steinberg group (Lie theory)">Steinberg groups</a> construct the unitary groups 2An, while the other orthogonal groups are constructed as 2Dn, where in both cases this refers to combining a diagram automorphism with a field automorphism. This also yields additional exotic Lie groups 2E6 and 3D4, the latter only defined over fields with an order 3 automorphism. The additional diagram automorphisms in positive characteristic yield the <a href="/wiki/Suzuki%E2%80%93Ree_group" class="mw-redirect" title="Suzuki–Ree group">Suzuki–Ree groups</a>, 2B2, 2F4, and 2G2. <div class="mw-heading mw-heading3"><h3 id="Folding">Folding</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=10" title="Edit section: Folding">edit</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Geometric_folding_Dynkin_graphs2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/4/4d/Geometric_folding_Dynkin_graphs2.png" decoding="async" width="188" height="164" class="mw-file-element" data-file-width="188" data-file-height="164" /></a><figcaption>Finite Coxeter group foldings.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Geometric_folding_Dynkin_graphs_affine2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/a6/Geometric_folding_Dynkin_graphs_affine2.png" decoding="async" width="343" height="384" class="mw-file-element" data-file-width="343" data-file-height="384" /></a><figcaption>Affine Coxeter group foldings, with three naming conventions: first, the original extended set; the second used in the context of <a href="/wiki/Quiver_(mathematics)" title="Quiver (mathematics)">quiver</a> graphs; and the last by <a href="/wiki/Victor_Kac" title="Victor Kac">Victor Kac</a> for <a href="/wiki/Affine_Lie_algebra#Constructing_the_Dynkin_diagrams" title="Affine Lie algebra">twisted affine Lie algebras</a>.</figcaption></figure> A (simply-laced) Dynkin diagram (finite or <a href="/wiki/Affine_Dynkin_diagram" class="mw-redirect" title="Affine Dynkin diagram">affine</a>) that has a symmetry (satisfying one condition, below) can be quotiented by the symmetry, yielding a new, generally multiply laced diagram, with the process called folding (due to most symmetries being 2-fold). At the level of Lie algebras, this corresponds to taking the invariant subalgebra under the outer automorphism group, and the process can be defined purely with reference to root systems, without using diagrams.<a href="#cite_note-10">[9]</a> Further, every multiply laced diagram (finite or infinite) can be obtained by folding a simply-laced diagram.<a href="#cite_note-stembridge-11">[10]</a> The one condition on the automorphism for folding to be possible is that distinct nodes of the graph in the same orbit (under the automorphism) must not be connected by an edge; at the level of root systems, roots in the same orbit must be orthogonal.<a href="#cite_note-stembridge-11">[10]</a> At the level of diagrams, this is necessary as otherwise the quotient diagram will have a loop, due to identifying two nodes but having an edge between them, and loops are not allowed in Dynkin diagrams. The nodes and edges of the quotient ("folded") diagram are the orbits of nodes and edges of the original diagram; the edges are single unless two incident edges map to the same edge (notably at nodes of valence greater than 2) – a "branch point" of the map, in which case the weight is the number of incident edges, and the arrow points towards the node at which they are incident – "the branch point maps to the non-homogeneous point". For example, in D4 folding to G2, the edge in G2 points from the class of the 3 outer nodes (valence 1), to the class of the central node (valence 3). The foldings of finite diagrams are:<a href="#cite_note-12">[11]</a><a href="#cite_note-13">[note 2]</a> <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2n-1}\to C_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2n-1}\to C_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78069555d3d838a1b63c28f2de79fc1c4bcfd731" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.378ex; height:2.509ex;" alt="{\displaystyle A_{2n-1}\to C_{n}}" /></li></ul> <dl><dd>(The automorphism of A2n does not yield a folding because the middle two nodes are connected by an edge, but in the same orbit.)</dd></dl> <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{n+1}\to B_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{n+1}\to B_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f8ade8f53a5fa321467b71dc6cfafb0ba14584f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.84ex; height:2.509ex;" alt="{\displaystyle D_{n+1}\to B_{n}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{4}\to G_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{4}\to G_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/524661ae62bceb7cd0044c71e77cf25ec6697e85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.474ex; height:2.509ex;" alt="{\displaystyle D_{4}\to G_{2}}" /> (if quotienting by the full group or a 3-cycle, in addition to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{4}\to B_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{4}\to B_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb5dad6a191157405fecc3a68b9d68871dba7fce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.411ex; height:2.509ex;" alt="{\displaystyle D_{4}\to B_{3}}" /> in 3 different ways, if quotienting by an involution)</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{6}\to F_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{6}\to F_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48162dfb509f75eda38c9c68f877adfba2deb36f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.932ex; height:2.509ex;" alt="{\displaystyle E_{6}\to F_{4}}" /></li></ul> Similar foldings exist for affine diagrams, including: <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{2n-1}\to {\tilde {C}}_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{2n-1}\to {\tilde {C}}_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cd1ddc5a2e71fe1dfc1c1372f35330a49437ff9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.515ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{2n-1}\to {\tilde {C}}_{n}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{n+1}\to {\tilde {B}}_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{n+1}\to {\tilde {B}}_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da84f68b571c18f96076648874c12a635e8c6ed2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.84ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{n+1}\to {\tilde {B}}_{n}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{4}\to {\tilde {G}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>G</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{4}\to {\tilde {G}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eaf9ed1802e7a02f744245a074b51da314e05607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.474ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{4}\to {\tilde {G}}_{2}}" /></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{6}\to {\tilde {F}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{6}\to {\tilde {F}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ef9b8de19456ef0deac863ef495704d858b15f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.303ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{6}\to {\tilde {F}}_{4}}" /></li></ul> The notion of foldings can also be applied more generally to <a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagrams</a><a href="#cite_note-14">[12]</a> – notably, one can generalize allowable quotients of Dynkin diagrams to Hn and I2(p). Geometrically this corresponds to projections of <a href="/wiki/Uniform_polytope" title="Uniform polytope">uniform polytopes</a>. Notably, any simply laced Dynkin diagram can be folded to I2(h), where h is the <a href="/wiki/Coxeter_number" class="mw-redirect" title="Coxeter number">Coxeter number</a>, which corresponds geometrically to projection to the <a href="/wiki/Coxeter_plane" class="mw-redirect" title="Coxeter plane">Coxeter plane</a>. Folding can be applied to reduce questions about (semisimple) Lie algebras to questions about simply-laced ones, together with an automorphism, which may be simpler than treating multiply laced algebras directly; this can be done in constructing the semisimple Lie algebras, for instance. See <a rel="nofollow" class="external text" href="https://mathoverflow.net/q/3888">Math Overflow: Folding by Automorphisms</a> for further discussion. <div class="mw-heading mw-heading2"><h2 id="Other_maps_of_diagrams">Other maps of diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=11" title="Edit section: Other maps of diagrams">edit</a>]</div> <table class="wikitable" align="right"> <tbody><tr align="center"> <td><a href="/wiki/File:Root_system_A2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/160px-Root_system_A2.svg.png" decoding="async" width="160" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/240px-Root_system_A2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Root_system_A2.svg/320px-Root_system_A2.svg.png 2x" data-file-width="600" data-file-height="600" /></a> A2 root system </td> <td><a href="/wiki/File:Root_system_G2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Root_system_G2.svg/250px-Root_system_G2.svg.png" decoding="async" width="160" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Root_system_G2.svg/330px-Root_system_G2.svg.png 2x" data-file-width="600" data-file-height="600" /></a> G2 root system </td></tr></tbody></table> Some additional maps of diagrams have meaningful interpretations, as detailed below. However, not all maps of root systems arise as maps of diagrams.<a href="#cite_note-armstrong-15">[13]</a> For example, there are two inclusions of root systems of A2 in G2, either as the six long roots or the six short roots. However, the nodes in the G2 diagram correspond to one long root and one short root, while the nodes in the A2 diagram correspond to roots of equal length, and thus this map of root systems cannot be expressed as a map of the diagrams. Some inclusions of root systems can be expressed as one diagram being an <a href="/wiki/Induced_subgraph" title="Induced subgraph">induced subgraph</a> of another, meaning "a subset of the nodes, with all edges between them". This is because eliminating a node from a Dynkin diagram corresponds to removing a simple root from a root system, which yields a root system of rank one lower. By contrast, removing an edge (or changing the multiplicity of an edge) while leaving the nodes unchanged corresponds to changing the angles between roots, which cannot be done without changing the entire root system. Thus, one can meaningfully remove nodes, but not edges. Removing a node from a connected diagram may yield a connected diagram (simple Lie algebra), if the node is a leaf, or a disconnected diagram (semisimple but not simple Lie algebra), with either two or three components (the latter for Dn and En). At the level of Lie algebras, these inclusions correspond to sub-Lie algebras. The maximal subgraphs are as follows; subgraphs related by a <a href="#Automorphisms">diagram automorphism</a> are labeled "conjugate": <ul><li>An+1: An, in 2 conjugate ways.</li> <li>Bn+1: An, Bn.</li> <li>Cn+1: An, Cn.</li> <li>Dn+1: An (2 conjugate ways), Dn.</li> <li>En+1: An, Dn, En. <ul><li>For E6, two of these coincide: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {D} _{5}\cong \mathrm {E} _{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mo>≅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {D} _{5}\cong \mathrm {E} _{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e3cc63ec3ee2d1af0c0186313311952ea2dd785" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.565ex; height:2.509ex;" alt="{\displaystyle \mathrm {D} _{5}\cong \mathrm {E} _{5}}" /> and are conjugate.</li></ul></li> <li>F4: B3, C3.</li> <li>G2: A1, in 2 non-conjugate ways (as a long root or a short root).</li></ul> Finally, duality of diagrams corresponds to reversing the direction of arrows, if any:<a href="#cite_note-armstrong-15">[13]</a> Bn and Cn are dual, while F4, and G2 are self-dual, as are the simply-laced ADE diagrams. <div class="mw-heading mw-heading2"><h2 id="Simply_laced">Simply laced</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=12" title="Edit section: Simply laced">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Simply_Laced_Dynkin_Diagrams.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Simply_Laced_Dynkin_Diagrams.svg/170px-Simply_Laced_Dynkin_Diagrams.svg.png" decoding="async" width="170" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Simply_Laced_Dynkin_Diagrams.svg/255px-Simply_Laced_Dynkin_Diagrams.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Simply_Laced_Dynkin_Diagrams.svg/340px-Simply_Laced_Dynkin_Diagrams.svg.png 2x" data-file-width="400" data-file-height="480" /></a><figcaption>The simply laced Dynkin diagrams classify diverse mathematical objects; this is called the <a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a>.</figcaption></figure> A Dynkin diagram with no multiple edges is called simply laced, as are the corresponding Lie algebra and Lie group. These are the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{n},D_{n},E_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n},D_{n},E_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8911cc31408f119b78cdc006cd73dc267fb85eff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.106ex; height:2.509ex;" alt="{\displaystyle A_{n},D_{n},E_{n}}" /> diagrams, and phenomena that such diagrams classify are referred to as an <a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a>. In this case the Dynkin diagrams exactly coincide with Coxeter diagrams, as there are no multiple edges. <div class="mw-heading mw-heading2"><h2 id="Satake_diagrams">Satake diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=13" title="Edit section: Satake diagrams">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Satake_diagram" title="Satake diagram">Satake diagram</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 1.5x" data-file-width="44" data-file-height="31" /></a></td><td class="mbox-text"><div class="mbox-text-span">This section needs expansion. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Dynkin_diagram&action=edit&section=">adding to it</a>. (December 2009)</div></td></tr></tbody></table> Dynkin diagrams classify complex semisimple Lie algebras. Real semisimple Lie algebras can be classified as <a href="/wiki/Real_form_(Lie_theory)" title="Real form (Lie theory)">real forms</a> of complex semisimple Lie algebras, and these are classified by <a href="/wiki/Satake_diagram" title="Satake diagram">Satake diagrams</a>, which are obtained from the Dynkin diagram by labeling some vertices black (filled), and connecting some other vertices in pairs by arrows, according to certain rules. <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=14" title="Edit section: History">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Semisimple_Lie_algebra#History" title="Semisimple Lie algebra">Semisimple Lie algebra § History</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Eugene_Dynkin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Eugene_Dynkin.jpg/250px-Eugene_Dynkin.jpg" decoding="async" width="170" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Eugene_Dynkin.jpg/255px-Eugene_Dynkin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e8/Eugene_Dynkin.jpg 2x" data-file-width="283" data-file-height="298" /></a><figcaption><a href="/wiki/Eugene_Dynkin" title="Eugene Dynkin">Eugene Dynkin</a>.</figcaption></figure> Dynkin diagrams are named for <a href="/wiki/Eugene_Dynkin" title="Eugene Dynkin">Eugene Dynkin</a>, who used them in two papers (1946, 1947) simplifying the classification of semisimple Lie algebras;<a href="#cite_note-knapp-16">[14]</a> see (<a href="#CITEREFDynkin2000">Dynkin 2000</a>). When Dynkin left the Soviet Union in 1976, which was at the time considered tantamount to treason, Soviet mathematicians were directed to refer to "diagrams of simple roots" rather than use his name.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Undirected graphs had been used earlier by Coxeter (1934) to classify <a href="/wiki/Reflection_group" title="Reflection group">reflection groups</a>, where the nodes corresponded to simple reflections; the graphs were then used (with length information) by Witt (1941) in reference to root systems, with the nodes corresponding to simple roots, as they are used today.<a href="#cite_note-knapp-16">[14]</a><a href="#cite_note-overdraw-17">[15]</a> Dynkin then used them in 1946 and 1947, acknowledging Coxeter and Witt in his 1947 paper. <div class="mw-heading mw-heading2"><h2 id="Conventions">Conventions</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=15" title="Edit section: Conventions">edit</a>]</div> Dynkin diagrams have been drawn in a number of ways;<a href="#cite_note-overdraw-17">[15]</a> the convention followed here is common, with 180° angles on nodes of valence 2, 120° angles on the valence 3 node of Dn, and 90°/90°/180° angles on the valence 3 node of En, with multiplicity indicated by 1, 2, or 3 parallel edges, and root length indicated by drawing an arrow on the edge for orientation. Beyond simplicity, a further benefit of this convention is that diagram automorphisms are realized by Euclidean isometries of the diagrams. Alternative convention include writing a number by the edge to indicate multiplicity (commonly used in Coxeter diagrams), darkening nodes to indicate root length, or using 120° angles on valence 2 nodes to make the nodes more distinct. There are also conventions about numbering the nodes. The most common modern convention had developed by the 1960s and is illustrated in (<a href="#CITEREFBourbaki1968">Bourbaki 1968</a>).<a href="#cite_note-overdraw-17">[15]</a> <div class="mw-heading mw-heading2"><h2 id="Rank_2_Dynkin_diagrams">Rank 2 Dynkin diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=16" title="Edit section: Rank 2 Dynkin diagrams">edit</a>]</div> Dynkin diagrams are equivalent to generalized <a href="/wiki/Cartan_matrix" title="Cartan matrix">Cartan matrices</a>, as shown in this table of rank 2 Dynkin diagrams with their corresponding 2 × 2 Cartan matrices. For rank 2, the Cartan matrix form is: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=\left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f0c38b6f92dd343e402c1f09e8a077371712646" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.583ex; height:6.176ex;" alt="{\displaystyle A=\left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}" /></dd></dl> A multi-edged diagram corresponds to the nondiagonal Cartan matrix elements ⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -a_{21},-a_{12}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>,</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -a_{21},-a_{12}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68de36028329ddad939e8fb7cd313d3e219f333c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.862ex; height:2.343ex;" alt="{\displaystyle -a_{21},-a_{12}}" />⁠, with the number of edges drawn equal to ⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \max(-a_{21},-a_{12})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">max</mo> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>,</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \max(-a_{21},-a_{12})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d6896539a7b0c70591928587d20bc18df5cf294" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.997ex; height:2.843ex;" alt="{\displaystyle \max(-a_{21},-a_{12})}" />⁠, and an arrow pointing towards nonunity elements. A generalized Cartan matrix is a <a href="/wiki/Square_matrix" title="Square matrix">square matrix</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=(a_{ij})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=(a_{ij})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/296ad42d9541f8285979ce822ccb661da56111ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.358ex; height:3.009ex;" alt="{\displaystyle A=(a_{ij})}" /> such that: <ol><li>For diagonal entries, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ii}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ii}=2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f816c6dd8f090528da77b8435080e4d2c5268dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.858ex; height:2.509ex;" alt="{\displaystyle a_{ii}=2}" />.</li> <li>For non-diagonal entries, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ij}\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ij}\leq 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/816e58f45a0362d5dab47a43881fd5bc59a630c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.968ex; height:2.843ex;" alt="{\displaystyle a_{ij}\leq 0}" />.</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ij}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ij}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a565e93211d1ad5c06a571ff8952ab3dfcff3638" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.968ex; height:2.843ex;" alt="{\displaystyle a_{ij}=0}" /> if and only if <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ji}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ji}=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d059b9aad48129a1907d2354eeeaa865847952e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.968ex; height:2.843ex;" alt="{\displaystyle a_{ji}=0}" /></li></ol> The Cartan matrix determines whether the group is of finite type (if it is a <a href="/wiki/Positive-definite_matrix" class="mw-redirect" title="Positive-definite matrix">positive-definite matrix</a>, i.e. all eigenvalues are positive), of affine type (if it is not positive-definite but positive-semidefinite, i.e. all eigenvalues are non-negative), or of indefinite type. The indefinite type often is further subdivided, for example a Coxeter group is Lorentzian if it has one negative eigenvalue and all other eigenvalues are positive. Moreover, multiple sources refer to hyberbolic Coxeter groups, but there are several non-equivalent definitions for this term. In the discussion below, hyperbolic Coxeter groups are a special case of Lorentzian, satisfying an extra condition. For rank 2, all negative determinant Cartan matrices correspond to hyperbolic Coxeter group. But in general, most negative determinant matrices are neither hyperbolic nor Lorentzian. Finite branches have <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (-a_{21},-a_{12})=(1,1),(2,1),(3,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>,</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (-a_{21},-a_{12})=(1,1),(2,1),(3,1)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8397cda259bf68fb97dceb3f4099c2afc9f0990d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.342ex; height:2.843ex;" alt="{\displaystyle (-a_{21},-a_{12})=(1,1),(2,1),(3,1)}" />, and affine branches (with a zero determinant) have ⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (-a_{21},-a_{12})=(2,2){\text{ or }}(4,1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>,</mo> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> or </mtext> </mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (-a_{21},-a_{12})=(2,2){\text{ or }}(4,1)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5efd127685054f46b9b7b1e8388b5416a481e40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.342ex; height:2.843ex;" alt="{\displaystyle (-a_{21},-a_{12})=(2,2){\text{ or }}(4,1)}" />⁠. <table class="wikitable skin-invert-image" width="720"> <caption>Rank 2 Dynkin diagrams </caption> <tbody><tr> <th rowspan="2">Group name </th> <th colspan="3">Dynkin diagram </th> <th colspan="2">Cartan matrix </th> <th rowspan="2">Symmetry order </th> <th rowspan="2">Related simply-laced group3 </th></tr> <tr> <th>(Standard) multi-edged graph <img src="//upload.wikimedia.org/wikipedia/commons/b/b7/Dyn2-node_n1.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/12/Dyn2-node_n2.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </th> <th>Valued graph1 </th> <th>Coxeter graph2 </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/609b9b4324da49c4903330c430b14203d6f971cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:11.741ex; height:6.176ex;" alt="{\displaystyle \left[{\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}}\right]}" /> </th> <th>Determinant ⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (4-a_{21}\cdot a_{12})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>4</mn> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (4-a_{21}\cdot a_{12})}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6576e4fa1408c2e1487adbf53a67c2aa921564b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.703ex; height:2.843ex;" alt="{\displaystyle (4-a_{21}\cdot a_{12})}" />⁠ </th></tr> <tr> <th colspan="5" style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: right;" class="table-rh"><a class="mw-selflink-fragment" href="#Finite_Dynkin_diagrams">Finite</a> </th> <td colspan="3">Determinant > 0 </td></tr> <tr align="center"> <th>A1xA1 </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&0\\0&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&0\\0&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58d402f7fd38428fe2ac791f5a5d12bf7832c69f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.108ex; height:3.343ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&0\\0&2\end{smallmatrix}}\right]}" /> </td> <td>4 </td> <td>2 </td> <td>  </td></tr> <tr align="center"> <th>A2 (undirected) </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18cb26b504d63dba11f3a12c7ee8fa25fe3bdf0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}}\right]}" /> </td> <td>3 </td> <td>3 </td> <td>  </td></tr> <tr align="center"> <th>B2 </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/58/Dyn-v21.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07ca67f2863fd2e6f5a6d91133f30d43a1c95805" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}}\right]}" /> </td> <td>2 </td> <td>4 </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2deec76778fda2b2f105b7448fb431e71427d91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle {A}_{3}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/66/Dyn-branch2.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /> </td></tr> <tr align="center"> <th>C2 </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/99/Dyn-v12.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>2</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a86fb5415f60aea3cee78429d52d340fc1df9ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}}\right]}" /> </td> <td>2 </td> <td>4 </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2deec76778fda2b2f105b7448fb431e71427d91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle {A}_{3}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>BC2 (undirected) </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-4.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {2}}\\-{\sqrt {2}}&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {2}}\\-{\sqrt {2}}&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/934421fb85592c1788a92b7d350953dd2ca94b5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.659ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {2}}\\-{\sqrt {2}}&2\end{smallmatrix}}\right]}" /> </td> <td>2 </td> <td>4 </td> <td> </td></tr> <tr align="center"> <th>G2 </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/42/Dyn-v13.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8008c32cde8626798763d8c84924571bffad4812" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}}\right]}" /> </td> <td>1 </td> <td>6 </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ab6d0954acdffa4cc14aa8e414da78b9cb0c8ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:2.509ex;" alt="{\displaystyle {D}_{4}}" /> <a href="/wiki/File:Dynkin_affine_D3_folding.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dynkin_affine_D3_folding.png" decoding="async" width="30" height="33" class="mw-file-element" data-file-width="30" data-file-height="33" /></a> </td></tr> <tr align="center"> <th>G2 (undirected) </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/2/22/Dyn-6.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/3/32/CDel_6.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {3}}\\-{\sqrt {3}}&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {3}}\\-{\sqrt {3}}&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b77e92921199a57f051014d4938de1a0d22ef38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.659ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-{\sqrt {3}}\\-{\sqrt {3}}&2\end{smallmatrix}}\right]}" /> </td> <td>1 </td> <td>6 </td> <td> </td></tr> <tr> <th colspan="5" style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: right;" class="table-rh"><a class="mw-selflink-fragment" href="#Affine_Dynkin_diagrams">Affine</a> </th> <td colspan="3">Determinant = 0 </td></tr> <tr align="center"> <th>A1(1) </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/ea/Dyn-4ab.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/76/Dyn-v22.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png" decoding="async" width="7" height="23" class="mw-file-element" data-file-width="7" data-file-height="23" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>2</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd86323eaf497d2bb96f757556dd458abd5863cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}}\right]}" /> </td> <td>0 </td> <td>∞ </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/740c3419432c6f9f8ffd2199ea5a5a109c20c096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{3}}" /> <a href="/wiki/File:Dynkin_affine_A3_folding.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dynkin_affine_A3_folding.png" decoding="async" width="28" height="24" class="mw-file-element" data-file-width="28" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>A2(2) </th> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6c/Dyn-4c.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/0/0f/Dyn-v14.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee764ce2933d720bd85ab4f4425789a0452bb97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}}\right]}" /> </td> <td>0 </td> <td>∞ </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6a13d506a7e9a43f58d2a45b4b2494edf1963ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{4}}" /> <a href="/wiki/File:Dynkin_affine_D4_folding.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/05/Dynkin_affine_D4_folding.png" decoding="async" width="29" height="41" class="mw-file-element" data-file-width="29" data-file-height="41" /></a> </td></tr> <tr> <th colspan="5" style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: right;" class="table-rh">Hyperbolic </th> <td colspan="3">Determinant < 0 </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/63/Dyn-v51.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5f8667328ef032fcc28485f9498d0aa472592ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}}\right]}" /> </td> <td>−1 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/57/Dyn-v32.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-3&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-2\\-3&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de5c1b92cef68df449f22b4667b47f409865b4a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-3&2\end{smallmatrix}}\right]}" /> </td> <td>−2 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5b/Dyn-v61.png" decoding="async" width="22" height="25" class="mw-file-element" data-file-width="22" data-file-height="25" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-6&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>6</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-6&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/209a341193290b49c172a7b764b7c280f8a4e95e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-6&2\end{smallmatrix}}\right]}" /> </td> <td>−2 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/2/24/Dyn-v71.png" decoding="async" width="22" height="25" class="mw-file-element" data-file-width="22" data-file-height="25" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-7&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>7</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-7&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13892cd6e699b3c266c6f2c5155a7d3a81171728" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-7&2\end{smallmatrix}}\right]}" /> </td> <td>−3 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/3/30/Dyn-v42.png" decoding="async" width="22" height="25" class="mw-file-element" data-file-width="22" data-file-height="25" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-4&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-2\\-4&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3373a4f62ccb77cbfad04b43f2a9b57dc7fdc618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-2\\-4&2\end{smallmatrix}}\right]}" /> </td> <td>−4 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c5/Dyn-v81.png" decoding="async" width="22" height="25" class="mw-file-element" data-file-width="22" data-file-height="25" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-8&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>8</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-1\\-8&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/457a113c8f8ee31dbb097965abe5da05593e254b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-1\\-8&2\end{smallmatrix}}\right]}" /> </td> <td>−4 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/58/Dyn-v33.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-3\\-3&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-3\\-3&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58de83867bd03b11edff1e45a0f03073a287b066" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.921ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-3\\-3&2\end{smallmatrix}}\right]}" /> </td> <td>−5 </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr align="center"> <th> </th> <td colspan="2"><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/Dyn-vab.png" decoding="async" width="22" height="24" class="mw-file-element" data-file-width="22" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mo>−</mo> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>a</mi> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}}\right]}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f2eb2e6d752a7d458a6c9892cee665463ab8fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.852ex; height:4.843ex;" alt="{\displaystyle \left[{\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}}\right]}" /> </td> <td>⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4-ab<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mo>−</mo> <mi>a</mi> <mi>b</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4-ab<0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0edc5cf1215d2288b7c0b3e41d4bed966433d0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.491ex; height:2.343ex;" alt="{\displaystyle 4-ab<0}" />⁠ </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td> </td></tr> <tr> <td colspan="8"> Note1: For hyperbolic groups, (a12⋅a21>4), the multiedge style is abandoned in favor of an explicit labeling (a21, a12) on the edge. These are usually not applied to finite and affine graphs.<a href="#cite_note-18">[16]</a> Note2: For undirected groups, <a href="/wiki/Coxeter_diagram" class="mw-redirect" title="Coxeter diagram">Coxeter diagrams</a> are interchangeable. They are usually labeled by their order of symmetry, with order-3 implied with no label. Note3: Many multi-edged groups can be obtained from a higher ranked simply-laced group by applying a suitable <a class="mw-selflink-fragment" href="#Folding">folding operation</a>. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Finite_Dynkin_diagrams">Finite Dynkin diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=17" title="Edit section: Finite Dynkin diagrams">edit</a>]</div> <table class="wikitable skin-invert-image"> <caption>Finite Dynkin graphs with 1 to 9 nodes </caption> <tbody><tr align="center"> <th rowspan="2">Rank </th> <th colspan="4"><a href="/wiki/Classical_Lie_group" class="mw-redirect" title="Classical Lie group">Classical Lie groups</a> </th> <th colspan="2"><a href="/wiki/Exceptional_Lie_group" class="mw-redirect" title="Exceptional Lie group">Exceptional Lie groups</a> </th></tr> <tr> <th height="35"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{1+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{1+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/635f9a63da237d104118592b28c6deeddd71a1a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.076ex; height:2.509ex;" alt="{\displaystyle {A}_{1+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{2+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{2+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4449becf0f4ebee3ab41d71eda345fa9740288a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.097ex; height:2.509ex;" alt="{\displaystyle {B}_{2+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{2+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{2+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3551df0a3f25d85a839e968a4226d798f0073a53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.995ex; height:2.509ex;" alt="{\displaystyle {C}_{2+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{2+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{2+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7b0814aa7ab34cd8a611e6ce1dd596c5fd1512a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.257ex; height:2.509ex;" alt="{\displaystyle {D}_{2+}}" /> </th> <th><a href="/wiki/En_(Lie_algebra)" title="En (Lie algebra)"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{3-8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>−</mo> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{3-8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed679a49f16a0066c27d54360cea64f1ee42529" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.87ex; height:2.509ex;" alt="{\displaystyle {E}_{3-8}}" /></a> </th> <th><a href="/wiki/G2_(mathematics)" title="G2 (mathematics)"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {G}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {G}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ac1787b17861db149af91a67a5bc3e194c8e9c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.881ex; height:2.509ex;" alt="{\displaystyle {G}_{2}}" /></a> / <a href="/wiki/F4_(mathematics)" title="F4 (mathematics)"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {F}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {F}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be0c56e02acb0e933648ee93675734cf2745158c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.549ex; height:2.509ex;" alt="{\displaystyle {F}_{4}}" /></a> </th></tr> <tr align="center"> <th>1 </th> <td>A1  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td> <td>  </td> <td>  </td> <td>  </td> <td>  </td></tr> <tr align="center"> <th>2 </th> <td>A2  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B2 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C2=B2 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D2=A1A1 <img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td> <td>G2  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/3/38/Dyn2-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>3 </th> <td>A3 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B3 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C3 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D3=A3 <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E3=A2A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td></tr> <tr align="center"> <th>4 </th> <td>A4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D4 <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E4=A4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>F4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>5 </th> <td>A5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D5 <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E5=D5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>6 </th> <td>A6  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B6  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C6  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D6  <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E6  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>7 </th> <td>A7  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B7  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C7  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D7  <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E7  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>8 </th> <td>A8  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B8  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C8  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D8  <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E8  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>9 </th> <td>A9  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>B9  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C9  <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D9  <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>10+ </th> <td>.. </td> <td>.. </td> <td>.. </td> <td>.. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Affine_Dynkin_diagrams">Affine Dynkin diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=18" title="Edit section: Affine Dynkin diagrams">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Affine_root_system" title="Affine root system">Affine root system</a></div> There are extensions of Dynkin diagrams, namely the affine Dynkin diagrams; these classify Cartan matrices of <a href="/wiki/Affine_Lie_algebra" title="Affine Lie algebra">affine Lie algebras</a>. These are classified in (<a href="#CITEREFKac1994">Kac 1994</a>, Chapter 4, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kuEjSb9teJwC&pg=PA47">pp. 47–</a>), specifically listed on (<a href="#CITEREFKac1994">Kac 1994</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kuEjSb9teJwC&pg=PA53">pp. 53–55</a>). Affine diagrams are denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{l}^{(1)},X_{l}^{(2)},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{l}^{(1)},X_{l}^{(2)},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ff6751c7e507315f787abb2306f4c44019b09c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.342ex; height:3.676ex;" alt="{\displaystyle X_{l}^{(1)},X_{l}^{(2)},}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{l}^{(3)},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{l}^{(3)},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e697c9be8422453363aaa02511ac7cfb4f10594" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.977ex; height:3.676ex;" alt="{\displaystyle X_{l}^{(3)},}" /> where X is the letter of the corresponding finite diagram, and the exponent depends on which series of affine diagrams they are in. The first of these, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{l}^{(1)},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{l}^{(1)},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef95a6bb377d9c279b5c19061b6dfc69bcd7cb3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.977ex; height:3.676ex;" alt="{\displaystyle X_{l}^{(1)},}" /> are most common, and are called extended Dynkin diagrams and denoted with a <a href="/wiki/Tilde" title="Tilde">tilde</a>, and also sometimes marked with a + superscript.<a href="#cite_note-19">[17]</a> as in <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{5}=A_{5}^{(1)}=A_{5}^{+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mo>=</mo> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{5}=A_{5}^{(1)}=A_{5}^{+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0481753ed4214d120f24423e74bf75aa60889910" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.357ex; height:3.676ex;" alt="{\displaystyle {\tilde {A}}_{5}=A_{5}^{(1)}=A_{5}^{+}}" />. The (2) and (3) series are called twisted affine diagrams. See <a rel="nofollow" class="external text" href="http://lesha.goder.com/dynkin-diagrams.html">Dynkin diagram generator</a> for diagrams. <table class="wikitable skin-invert-image" width="840"> <tbody><tr align="center"> <td><a href="/wiki/File:Affine_Dynkin_diagrams.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Affine_Dynkin_diagrams.png/420px-Affine_Dynkin_diagrams.png" decoding="async" width="420" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Affine_Dynkin_diagrams.png/630px-Affine_Dynkin_diagrams.png 1.5x, //upload.wikimedia.org/wikipedia/commons/5/50/Affine_Dynkin_diagrams.png 2x" data-file-width="693" data-file-height="265" /></a> The set of extended affine Dynkin diagrams, with added nodes in green (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73136e4a27fe39c123d16a7808e76d3162ce42bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 3}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f568bf6d34e97b9fdda0dc7e276d6c4501d2045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.982ex; height:2.509ex;" alt="{\displaystyle B_{n}}" /> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 4}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25010fec4b0f68f1b46f49d14917d962acca0b16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 4}" /> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{n}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe03857347bf517e7fbda4085b0dafd6018cf18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.143ex; height:2.509ex;" alt="{\displaystyle D_{n}}" />) </td> <td><a href="/wiki/File:Twisted_affine_Dynkin_diagrams.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Twisted_affine_Dynkin_diagrams.png/330px-Twisted_affine_Dynkin_diagrams.png" decoding="async" width="320" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0c/Twisted_affine_Dynkin_diagrams.png 1.5x" data-file-width="429" data-file-height="223" /></a> "Twisted" affine forms are named with (2) or (3) superscripts. (The subscript k always counts the number of yellow nodes in the graph, i.e. the total number of nodes minus 1.) </td></tr></tbody></table> Here are all of the Dynkin graphs for affine groups up to 10 nodes. Extended Dynkin graphs are given as the ~ families, the same as the finite graphs above, with one node added. Other directed-graph variations are given with a superscript value (2) or (3), representing foldings of higher order groups. These are categorized as Twisted affine diagrams.<a href="#cite_note-20">[18]</a> <table class="wikitable skin-invert-image"> <caption>Connected affine Dynkin graphs up to (2 to 10 nodes) (Grouped as undirected graphs) </caption> <tbody><tr> <th>Rank </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{1+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{1+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cde0b578fb44c537001f9aab898a2ecd6bbdffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.108ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{1+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{3+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{3+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/211378b24e2556146f530eaf5c4cfa82af0237ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.097ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{3+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{2+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{2+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea4e8ec02c962dabc42aa668969e5bde07c6eb13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.099ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{2+}}" /> </th> <th><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{4+}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mo>+</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{4+}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0360d732cc34f95ccdc6a53a638615152a990cbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.257ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{4+}}" /> </th> <th>E / F / G </th></tr> <tr align="center" valign="top"> <th>2 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/843d8e4a4af55a35f5f77f73bad8fdc1a5461261" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{1}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{1}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{1}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c52737cd338e12ee49ddaad5a0b48583aed2d96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{1}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/ea/Dyn-4ab.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td rowspan="2">  </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{2}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{2}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee8f8dc32617a205a2c6d443dca9b289551c86ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{2}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6c/Dyn-4c.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td rowspan="3">  </td> <td>  </td></tr> <tr align="center" valign="top"> <th>3 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5fc67207a38d6b502cb105b00723897960407d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{2}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{2}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{2}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35929b816a3e6c8338769672669ba374b5d3ba2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{2}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinA2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5602e1d29d9bbab64fa3e44a7910ab1ffcce6d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{2}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{2}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{2}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feb8f0a60d5061445d6d7f8ba8f40fb97aff25ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{2}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinC2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{5}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{5}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fbfa805410638ddfb572058fed4565a181b7b1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{5}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{4}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{4}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0e7b2512fccc5b9d1467ca9d216c11a98e3a571" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{4}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {G}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>G</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {G}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fffeca164163637e88208f3286179052dc8b6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.881ex; height:3.009ex;" alt="{\displaystyle {\tilde {G}}_{2}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {G}_{2}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {G}_{2}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/073059352748585f52aedbd09033043b8797e682" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.16ex; height:3.676ex;" alt="{\displaystyle {G}_{2}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinG2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/3/38/Dyn2-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{4}^{(3)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{4}^{(3)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb7528efae419323bc671ce03db2e62955fe5ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{4}^{(3)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/98/Dyn2-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>4 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/740c3419432c6f9f8ffd2199ea5a5a109c20c096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{3}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{3}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{3}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c3526491f1af89b54b08d1aedd08dc10ae0c8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{3}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinA3Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Dyn2-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78dcfcbc21ab3387f1f95f268d6e6cbcfcebcc69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{3}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{3}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{3}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e72cde8d3e9144daa1be820deb626335e5dcddec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{3}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinB3Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{5}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{5}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/769b27891d27fe34c042edbf3cb55b4ce7810af6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{5}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58f6155c77ccc8f6acc9a64d6b2d78e025897f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{3}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{3}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{3}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba44a3e215ce7f2dcdb5fa0cf754999b3ec31d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{3}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinC3Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{6}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{6}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1d6e980522a3edbe931ee091dfa6974facf242" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{6}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{6}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{6}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e4a43e34917964bcc0383f2438499586c97b4c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{6}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td></tr> <tr align="center" valign="top"> <th>5 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa04789c3ba56768276d72b5957e8b72fe05909a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{4}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{4}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{4}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9d7996073d4ebf906fb5aaa080f1e049ddcbefc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{4}^{(1)}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinA4Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7160090323416d0ba77fb3b2782f3f79e23eeab9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{4}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{4}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{4}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecb1675bc384bb4cf32301958aa5984b0605362b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{4}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinB4Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{7}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{7}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fff954da596551fe037590b96a1868a8971c4139" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{7}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/404d24500dbc31cb7df8b26172d5e64d2f7b09cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{4}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{4}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{4}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b8c37cbd52f25b4704e46b44b595186fc6b14cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{4}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinC4Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{7}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{7}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63d7f9ec15020b7a6047fb622d39cb379b3220ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{7}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{8}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{8}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64645b1991f80311fd22856f247be97ff4d27396" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{8}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6a13d506a7e9a43f58d2a45b4b2494edf1963ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{4}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{4}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{4}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43b4d29d337ad5f4e4441161577383594df178bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{4}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinD4Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {F}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {F}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f20867779350876839191b841386e4f563660530" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.859ex; height:3.009ex;" alt="{\displaystyle {\tilde {F}}_{4}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {F}_{4}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {F}_{4}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bcb916c4d0df30a44cafca0e8a9f3e36c57ccdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.148ex; height:3.676ex;" alt="{\displaystyle {F}_{4}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinF42Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{6}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{6}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ad5c94970befcd1fc2cd16d308a305565c75c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.127ex; height:3.676ex;" alt="{\displaystyle {E}_{6}^{(2)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>6 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2aafa82373817e59ec217f474a90ff4d300db8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{5}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{5}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{5}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ff3fe8198bcf3e45db3704a6624edacb62003b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{5}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinA5Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Dyn2-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b08bd9d1bc5b205fafedb2faea772e17ba2219b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{5}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{5}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{5}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d63f05acf5fbf24c162434bd911ba3cde878306d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{5}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinB5Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{9}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{9}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2df28fb66e504f3bbf565681859f91a128282675" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{9}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73e874213407a3087a36c812a444e0737e9386db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{5}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{5}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{5}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd161a9afa8e20c7bbd7065ac34f351f90a9e5e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{5}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinC5Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{8}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{8}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/982aa3107f0aca2ba746263e07c86c0e756dd15e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{8}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{10}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{10}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42d5bc21c947173f45da85a67ad36a5b5376875d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{10}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d978c4890992fd704387e9de35a53617b3d2a0fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{5}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{5}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{5}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac317197e926cd2d6d59bedecf7e2df4c13e70a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{5}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinD5Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /></a> </td> <td>  </td></tr> <tr align="center" valign="top"> <th>7 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53b068aa3dd34a1d82b4d8a5df9567ab98af4f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{6}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{6}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{6}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26467fe5bf47143304c86fab6ec90676e391cbb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{6}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineA6.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eaaede34474009ef0e0dc5e08ec167d02284abe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{6}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{6}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{6}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5033c1b6cab50dccab3c1321c5e5643e9b9ea3ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{6}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{11}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{11}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5375211df546020c7584935c2d08be7146423408" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{11}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5060e8e531490ce828db248835863906f3de7728" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{6}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{6}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{6}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93766c6186e0dbc4f463881d181099762cb3644e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{6}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{9}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{9}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99a46020514ff17e9c9babc1ef2d5d33387482e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{9}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{12}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{12}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/250a8068bf78faacd796a62ebab5e69d0ddf42a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{12}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efe178ef06085e28adc41d582a145f8db72d1e72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{6}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{6}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{6}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829f70a989106cf31c78102d97c27705d68eca32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{6}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6f88e9053912a19c4fc76340931dd573140944e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{6}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{6}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{6}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/191750f38413a38ea9290bf0ac62c830ae5ff097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.127ex; height:3.676ex;" alt="{\displaystyle {E}_{6}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>8 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/716822fdda39c78c6452810d3457fb0c5ba465e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{7}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{7}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{7}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee623e0604b404a524f8fef04e3945780f8ce92b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{7}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineA7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Dyn2-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec698618eea8492fdf9d3be6d782c2be08f198a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{7}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{7}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{7}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96bed409020e92b14b1014c4809fcfc5a0b9f0c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{7}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineB7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{13}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>13</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{13}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52311cd478b40f75c493480353a9256d07913801" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{13}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/938064dcd1a724c552664ef31a9259239a3fc24c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{7}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{7}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{7}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/255652d9c26e473b0057ccc345fe2b9fcd5f1c9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{7}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{10}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{10}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d37ae1ceb7cda2d2f4303f0430d04ccdd98793fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{10}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{14}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>14</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{14}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/234f63b71f666c5815dbe1387bb757e9ca8af966" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{14}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16284ee83632a600f9eec9c27a351b806d25e44c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{7}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{7}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{7}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/757f186558f722dc8b1c11384d560a8a1882bcd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{7}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineD7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c251975c254e8e74513a013145d6ec2b0e5d016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{7}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{7}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{7}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71a762c0262cddb9f0c7d1a3d94caa609263a364" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.127ex; height:3.676ex;" alt="{\displaystyle {E}_{7}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/5/50/Dyn-nodesyg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>9 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9d3da41f7903f33c85a1eb534488af013fa02d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{8}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{8}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{8}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cf6046dea1efdec89ccd9ab8110bbb976f87b9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{8}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineA8.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d88a859bc947d56cf66169005b00b921575dd9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{8}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{8}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{8}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/191083e0f05131b0769fa80bac746f15dac217d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{8}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{15}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>15</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{15}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd448c891c9686fc66855a0628d991b3af0ae634" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{15}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5965b88fc07793cd73c25699d4bb68478d1bc4a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{8}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{8}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{8}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5689203efb3441fa40466fd4d2144bca8c9fae87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{8}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{11}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{11}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c0d01ec7dba27b089bf5109a28b59817386ab5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{11}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{16}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>16</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{16}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/174adfe849fc642d4572cccb44fe4767a887acb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{16}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdd08f8352da04362404ee80c273997c3b968891" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{8}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{8}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{8}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0290b4c6d554f83e76b4b8d5f28d7843218d182b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{8}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7960ec54a7dac08a847e38ee3137a3e95a9044" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{8}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{8}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{8}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42f4ae851a1a0660762cdbd22076c1dd64df813b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.127ex; height:3.676ex;" alt="{\displaystyle {E}_{8}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>10 </th> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{9}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{9}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce9d67cae17d395d0d11fae86ba7fd6682fae659" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{9}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{9}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{9}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45a785832c56a6c816161df13090bd8e7db62b63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{9}^{(1)}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineA9.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Dyn2-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Dyn2-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{9}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{9}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0792bb45481ba34eb8073233e7d49df25a4f7563" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{9}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {B}_{9}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {B}_{9}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a383c434d9015cd5222c3e8254881bbba8123ef8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.098ex; height:3.676ex;" alt="{\displaystyle {B}_{9}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{17}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>17</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{17}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da64898d6d441517cd1bcedecb7f4c310020a79b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{17}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/8/81/Dyn-branch1yg.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{9}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{9}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7121b32d598215f61f0c54f9c04668c4391e7c69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{9}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {C}_{9}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {C}_{9}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9beb5b4f80ad2642741c505cc695bb20fbda8f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.131ex; height:3.676ex;" alt="{\displaystyle {C}_{9}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{12}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{12}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ee867faa2c554990b301927df829752a1f52d8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{12}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}_{18}^{(2)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>18</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}_{18}^{(2)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b27290630dccfe9a73fa4c5c07df6e200daa1d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.077ex; height:3.676ex;" alt="{\displaystyle {A}_{18}^{(2)}}" />: <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{9}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{9}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ec879abb90b050707c0109c3ba047c697e7c40b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{9}}" /> or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}_{9}^{(1)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}_{9}^{(1)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9e882a857b7bef009e5ce89b390cd712668c6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.258ex; height:3.676ex;" alt="{\displaystyle {D}_{9}^{(1)}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/a/a1/Dyn-branch1.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/80/Dyn-branch2gy.png" decoding="async" width="16" height="24" class="mw-file-element" data-file-width="16" data-file-height="24" /> </td></tr> <tr align="center" valign="top"> <th>11 </th> <td>... </td> <td>... </td> <td>... </td> <td>... </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Hyperbolic_and_higher_Dynkin_diagrams">Hyperbolic and higher Dynkin diagrams</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=19" title="Edit section: Hyperbolic and higher Dynkin diagrams">edit</a>]</div> The set of compact and noncompact hyperbolic Dynkin graphs has been enumerated.<a href="#cite_note-21">[19]</a> All rank 3 hyperbolic graphs are compact. Compact hyperbolic Dynkin diagrams exist up to rank 5, and noncompact hyperbolic graphs exist up to rank 10. <table class="wikitable"> <caption>Summary </caption> <tbody><tr> <th>Rank </th> <th>Compact </th> <th>Noncompact </th> <th>Total </th></tr> <tr> <th>3 </th> <td>31</td> <td>93</td> <td>123 </td></tr> <tr> <th>4 </th> <td>3</td> <td>50</td> <td>53 </td></tr> <tr> <th>5 </th> <td>1</td> <td>21</td> <td>22 </td></tr> <tr> <th>6 </th> <td>0</td> <td>22</td> <td>22 </td></tr> <tr> <th>7 </th> <td>0</td> <td>4</td> <td>4 </td></tr> <tr> <th>8 </th> <td>0</td> <td>5</td> <td>5 </td></tr> <tr> <th>9 </th> <td>0</td> <td>5</td> <td>5 </td></tr> <tr> <th>10 </th> <td>0</td> <td>4</td> <td>4 </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Compact_hyperbolic_Dynkin_diagrams">Compact hyperbolic Dynkin diagrams</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=20" title="Edit section: Compact hyperbolic Dynkin diagrams">edit</a>]</div> <table class="wikitable skin-invert-image"> <caption>Compact hyperbolic graphs </caption> <tbody><tr> <th colspan="2">Rank 3 </th> <th>Rank 4 </th> <th>Rank 5 </th></tr> <tr valign="top"> <td>Linear graphs <ul><li>(6 4 2): <ul><li>H100(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H101(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H105(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H106(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li></ul></li> <li>(6 6 2): <ul><li>H114(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H115(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H116(3): <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li></ul></li></ul> </td> <td>Cyclic graphs <ul><li>(4 3 3): H1(3): <img src="//upload.wikimedia.org/wikipedia/commons/e/e0/Dyn-branch4al.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></li> <li>(4 4 3): 3 forms...</li> <li>(4 4 4): 2 forms...</li> <li>(6 3 3): H3(3): <img src="//upload.wikimedia.org/wikipedia/commons/9/9a/Dyn-branch6.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></li> <li>(6 4 3): 4 forms...</li> <li>(6 4 4): 4 forms...</li> <li>(6 6 3): 3 forms...</li> <li>(6 6 4): 4 forms...</li> <li>(6 6 6): 2 forms...</li></ul> </td> <td> <ul><li>(4 3 3 3): <ul><li>H8(4): <img src="//upload.wikimedia.org/wikipedia/commons/e/e0/Dyn-branch4al.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></li> <li>H13(4): <img src="//upload.wikimedia.org/wikipedia/commons/e/e0/Dyn-branch4al.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/56/Dyn-branch4ar.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /></li></ul></li> <li>(4 3 4 3): <ul><li>H14(4): <img src="//upload.wikimedia.org/wikipedia/commons/e/e0/Dyn-branch4al.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e7/Dyn-branch4br.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /></li></ul></li></ul> </td> <td> <ul><li>(4 3 3 3 3): <ul><li>H7(5): <img src="//upload.wikimedia.org/wikipedia/commons/e/e0/Dyn-branch4al.png" decoding="async" width="12" height="24" class="mw-file-element" data-file-width="12" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></li></ul></li></ul> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Noncompact_(over-extended)_forms">Noncompact (over-extended) forms</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=21" title="Edit section: Noncompact (over-extended) forms">edit</a>]</div> Some notations used in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, such as <a href="/wiki/M-theory" title="M-theory">M-theory</a>, use a "+" superscript for extended groups instead of a "~" and this allows higher extensions groups to be defined. <ol><li>Extended Dynkin diagrams (affine) are given "+" and represent one added node. (Same as "~")</li> <li>Over-extended Dynkin diagrams (hyperbolic) are given "^" or "++" and represent two added nodes.</li> <li>Very-extended Dynkin diagrams with 3 nodes added are given "+++".</li></ol> <table class="wikitable skin-invert-image"> <caption>Some example over-extended (hyperbolic) Dynkin diagrams </caption> <tbody><tr align="center"> <th>Rank </th> <th height="30">AEn = An-2(1)^ </th> <th height="30">BEn = Bn-2(1)^ CEn </th> <th height="30">Cn-2(1)^ </th> <th height="30">DEn = Dn-2(1)^ </th> <th>E / F / G </th></tr> <tr align="center"> <th>3 </th> <td>AE3:<img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/ea/Dyn-4ab.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td> <td>  </td> <td>  </td> <td>  </td></tr> <tr align="center"> <th>4 </th> <td>AE4:<img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>  </td> <td>C2(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A4(2)'^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A4(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> D3(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td rowspan="2">  </td> <td>G2(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/3/38/Dyn2-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> D4(3)^ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/98/Dyn2-6b.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>5 </th> <td>AE5:<img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>BE5 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE5 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C3(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A6(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A6(2)'^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> D5(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td></tr> <tr align="center"> <th>6 </th> <td>AE6 <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>BE6 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE6 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>C4(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A8(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> A8(2)'^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> D7(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>DE6 <img src="//upload.wikimedia.org/wikipedia/commons/0/02/Dyn-triplebranch1.png" decoding="async" width="24" height="24" class="mw-file-element" data-file-width="24" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>F4(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> E6(2)^ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>7 </th> <td>AE7 <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>BE7 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE7 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>DE7 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td></tr> <tr align="center"> <th>8 </th> <td>AE8 <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>BE8 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE8 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>DE8 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E6(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>9 </th> <td>AE9 <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>BE9 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE9 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>DE9 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E7(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>10 </th> <td>  </td> <td>BE10 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> CE10 <img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>DE10 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E10=E8(1)^ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="238_Hyperbolic_groups_(compact_and_noncompact)">238 Hyperbolic groups (compact and noncompact)</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=22" title="Edit section: 238 Hyperbolic groups (compact and noncompact)">edit</a>]</div> The 238 hyperbolic groups (compact and noncompact) of rank <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73136e4a27fe39c123d16a7808e76d3162ce42bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 3}" /> are named as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{i}^{(n)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{i}^{(n)}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/effebf1cd24c276940101d994eac05f7c18b2572" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.601ex; height:3.676ex;" alt="{\displaystyle H_{i}^{(n)}}" /> and listed as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=1,2,3...}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3...</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=1,2,3...}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e97b095ac3672cdcc8e2a39b16414c271b22fabc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.397ex; height:2.509ex;" alt="{\displaystyle i=1,2,3...}" /> for each rank. <ul class="gallery mw-gallery-nolines skin-invert-image" style="max-width: 836px;"> <li class="gallerybox" style="width: 205px"> <div class="thumb" style="width: 200px;"><a href="/wiki/File:Rank3CompactHyperbolicDynkins1-31bw.svg" 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//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Rank7HyperbolicDynkins221-224bw.svg/500px-Rank7HyperbolicDynkins221-224bw.svg.png 2x" data-file-width="1000" data-file-height="730" /></a></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 205px"> <div class="thumb" style="width: 200px;"><a href="/wiki/File:Rank8HyperbolicDynkins225-229bw.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Rank8HyperbolicDynkins225-229bw.svg/200px-Rank8HyperbolicDynkins225-229bw.svg.png" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Rank8HyperbolicDynkins225-229bw.svg/300px-Rank8HyperbolicDynkins225-229bw.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Rank8HyperbolicDynkins225-229bw.svg/400px-Rank8HyperbolicDynkins225-229bw.svg.png 2x" data-file-width="1000" data-file-height="1020" /></a></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 205px"> <div class="thumb" style="width: 200px;"><a href="/wiki/File:Rank9HyperbolicDynkins230-234bw.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Rank9HyperbolicDynkins230-234bw.svg/200px-Rank9HyperbolicDynkins230-234bw.svg.png" decoding="async" width="200" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Rank9HyperbolicDynkins230-234bw.svg/300px-Rank9HyperbolicDynkins230-234bw.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Rank9HyperbolicDynkins230-234bw.svg/400px-Rank9HyperbolicDynkins230-234bw.svg.png 2x" data-file-width="1000" data-file-height="910" /></a></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 205px"> <div class="thumb" style="width: 200px;"><a href="/wiki/File:Rank10HyperbolicDynkins235-238bw.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Rank10HyperbolicDynkins235-238bw.svg/200px-Rank10HyperbolicDynkins235-238bw.svg.png" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Rank10HyperbolicDynkins235-238bw.svg/300px-Rank10HyperbolicDynkins235-238bw.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Rank10HyperbolicDynkins235-238bw.svg/400px-Rank10HyperbolicDynkins235-238bw.svg.png 2x" data-file-width="1000" data-file-height="800" /></a></div> <div class="gallerytext"></div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Very-extended">Very-extended</h3>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=23" title="Edit section: Very-extended">edit</a>]</div> Very-extended groups are <a href="/wiki/Lorentz_group" title="Lorentz group">Lorentz groups</a>, defined by adding three nodes to the finite groups. The E8, E7, E6, F4, and G2 offer six series ending as very-extended groups. Other extended series not shown can be defined from An, Bn, Cn, and Dn, as different series for each n. The determinant of the associated <a href="/wiki/Cartan_matrix" title="Cartan matrix">Cartan matrix</a> determine where the series changes from finite (positive) to affine (zero) to a noncompact hyperbolic group (negative), and ending as a Lorentz group that can be defined with the use of one <a href="/wiki/Time-like" class="mw-redirect" title="Time-like">time-like</a> dimension, and is used in <a href="/wiki/M_theory" class="mw-redirect" title="M theory">M theory</a>.<a href="#cite_note-22">[20]</a> <table class="wikitable"> <caption>Rank 2 extended series </caption> <tbody><tr> <th>Finite </th> <th>A2 </th> <th>C2 </th> <th><a href="/wiki/G2_(mathematics)" title="G2 (mathematics)"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/645011b0c6933a02f5f7d84624f78220d747427e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.881ex; height:2.509ex;" alt="{\displaystyle G_{2}}" /></a> </th></tr> <tr align="center"> <th>2 </th> <td bgcolor="#ffffe0">A2<img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">C2<img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">G2<img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>3 </th> <td bgcolor="#ffe0e0">A2+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5fc67207a38d6b502cb105b00723897960407d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{2}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinA2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">C2+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5602e1d29d9bbab64fa3e44a7910ab1ffcce6d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{2}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinC2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">G2+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {G}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>G</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {G}}_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fffeca164163637e88208f3286179052dc8b6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.881ex; height:3.009ex;" alt="{\displaystyle {\tilde {G}}_{2}}" /><a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinG2Affine.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>4 </th> <td bgcolor="#e0ffe0">A2++<a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineA2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">C2++<a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineC2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">G2++<a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineG2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>5 </th> <td bgcolor="#e0e0ff">A2+++<a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineA2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0e0ff">C2+++<a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineC2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0e0ff">G2+++<a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineG2.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/6/6d/Dyn-6a.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>Det(Mn) </th> <td>3(3 − n) </td> <td>2(3 − n) </td> <td>3 − n </td></tr></tbody></table> <table class="wikitable"> <caption>Rank 3 and 4 extended series </caption> <tbody><tr> <th>Finite </th> <th>A3 </th> <th>B3 </th> <th>C3 </th> <th>A4 </th> <th>B4 </th> <th>C4 </th> <th>D4 </th> <th><a href="/wiki/F4_(mathematics)" title="F4 (mathematics)"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8718a2df1e70bea3cd21ab9e0cd45dc354818451" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.549ex; height:2.509ex;" alt="{\displaystyle F_{4}}" /></a> </th></tr> <tr align="center" bgcolor="#ddd"> <th>2 </th> <td> </td> <td>A12 <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/9a/Dyn-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td>A2 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" bgcolor="#ddd"> <th>3 </th> <td bgcolor="#ffffe0">A3 <img src="//upload.wikimedia.org/wikipedia/commons/6/6f/Dyn2-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">B3 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">C3 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>B2A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>A13 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>4 </th> <td bgcolor="#ffe0e0">A3+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/740c3419432c6f9f8ffd2199ea5a5a109c20c096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{3}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">B3+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78dcfcbc21ab3387f1f95f268d6e6cbcfcebcc69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{3}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">C3+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58f6155c77ccc8f6acc9a64d6b2d78e025897f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{3}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">A4 <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">B4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">C4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">D4 <img src="//upload.wikimedia.org/wikipedia/commons/0/02/Dyn-triplebranch1.png" decoding="async" width="24" height="24" class="mw-file-element" data-file-width="24" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">F4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>5 </th> <td bgcolor="#e0ffe0">A3++ <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">B3++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">C3++ <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">A4+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa04789c3ba56768276d72b5957e8b72fe05909a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{4}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">B4+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7160090323416d0ba77fb3b2782f3f79e23eeab9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{4}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">C4+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {C}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {C}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/404d24500dbc31cb7df8b26172d5e64d2f7b09cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.821ex; height:3.009ex;" alt="{\displaystyle {\tilde {C}}_{4}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">D4+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6a13d506a7e9a43f58d2a45b4b2494edf1963ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{4}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/0/02/Dyn-triplebranch1.png" decoding="async" width="24" height="24" class="mw-file-element" data-file-width="24" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">F4+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {F}}_{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {F}}_{4}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f20867779350876839191b841386e4f563660530" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.859ex; height:3.009ex;" alt="{\displaystyle {\tilde {F}}_{4}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>6 </th> <td bgcolor="#e0e0ff">A3+++ <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">B3+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">C3+++ <img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dyn-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Dyn-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">A4++ <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">B4++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">C4++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">D4++ <img src="//upload.wikimedia.org/wikipedia/commons/0/02/Dyn-triplebranch1.png" decoding="async" width="24" height="24" class="mw-file-element" data-file-width="24" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">F4++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>7 </th> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff">A4+++ <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">B4+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">C4+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a0/Dyn2-4b.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">D4+++ <img src="//upload.wikimedia.org/wikipedia/commons/0/02/Dyn-triplebranch1.png" decoding="async" width="24" height="24" class="mw-file-element" data-file-width="24" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">F4+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>Det(Mn) </th> <td>4(4 − n) </td> <td colspan="2">2(4 − n) </td> <td>5(5 − n) </td> <td colspan="2">2(5 − n) </td> <td>4(5 − n) </td> <td>5 − n </td></tr></tbody></table> <table class="wikitable"> <caption>Rank 5 and 6 extended series </caption> <tbody><tr> <th>Finite </th> <th>A5 </th> <th>B5 </th> <th>D5 </th> <th>A6 </th> <th>B6 </th> <th>D6 </th> <th>E6 </th></tr> <tr align="center" bgcolor="#ddd"> <th>4 </th> <td> </td> <td>B3A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>A3A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td> </td> <td> </td> <td>A22 <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" bgcolor="#ddd"> <th>5 </th> <td bgcolor="#ffffe0">A5 <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0"><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">D5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td> </td> <td>B4A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D4A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>A5 <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /> </td></tr> <tr align="center"> <th>6 </th> <td bgcolor="#ffe0e0">A5+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2aafa82373817e59ec217f474a90ff4d300db8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{5}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">B5+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b08bd9d1bc5b205fafedb2faea772e17ba2219b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{5}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">D5+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{5}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d978c4890992fd704387e9de35a53617b3d2a0fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{5}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">A6 <img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/Dyn2-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/Dyn2-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">B6 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">D6 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">E6 <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>7 </th> <td bgcolor="#e0ffe0">A5++ <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">B5++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">D5++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">A6+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53b068aa3dd34a1d82b4d8a5df9567ab98af4f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{6}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">B6+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eaaede34474009ef0e0dc5e08ec167d02284abe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{6}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">D6+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efe178ef06085e28adc41d582a145f8db72d1e72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{6}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffe0e0">E6+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{6}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6f88e9053912a19c4fc76340931dd573140944e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{6}}" /> <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>8 </th> <td bgcolor="#e0e0ff">A5+++ <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">B5+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">D5+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">A6++ <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">B6++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">D6++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0ffe0">E6++ <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>9 </th> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff">A6+++ <img src="//upload.wikimedia.org/wikipedia/commons/6/68/Dyn-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">B6+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">D6+++ <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#e0e0ff">E6+++ <img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/ff/Dyn-loop2.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/8/8b/Dyn-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center"> <th>Det(Mn) </th> <td>6(6 − n) </td> <td>2(6 − n) </td> <td>4(6 − n) </td> <td>7(7 − n) </td> <td>2(7 − n) </td> <td>4(7 − n) </td> <td>3(7 − n) </td></tr></tbody></table> <table class="wikitable"> <caption>Some rank 7 and higher extended series </caption> <tbody><tr> <th>Finite </th> <th>A7 </th> <th>B7 </th> <th>D7 </th> <th>E7 </th> <th><a href="/wiki/En_(Lie_algebra)" title="En (Lie algebra)">E8</a> </th></tr> <tr align="center" bgcolor="#ddd"> <th>3 </th> <td> </td> <td> </td> <td> </td> <td> </td> <td>E3=A2A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" bgcolor="#ddd"> <th>4 </th> <td> </td> <td> </td> <td> </td> <td>A3A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E4=A4 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" bgcolor="#ddd"> <th>5 </th> <td> </td> <td> </td> <td> </td> <td>A5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E5=D5 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td></tr> <tr align="center" bgcolor="#ddd"> <th>6 </th> <td> </td> <td>B5A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D5A1 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/Dyn2-2.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>D6 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td>E6 <a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinE6Full.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center" bgcolor="#ddd"> <th>7 </th> <td bgcolor="#ffffe0">A7 <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">B7 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">D7 <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /> </td> <td bgcolor="#ffffe0">E7 <a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinE7Full.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td>E7 <a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinE7Full.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>8 </th> <td bgcolor="#ffe0e0">A7+‍=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {A}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {A}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/716822fdda39c78c6452810d3457fb0c5ba465e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {A}}_{7}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineA7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">B7+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {B}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {B}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec698618eea8492fdf9d3be6d782c2be08f198a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:3.009ex;" alt="{\displaystyle {\tilde {B}}_{7}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineB7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">D7+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {D}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {D}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16284ee83632a600f9eec9c27a351b806d25e44c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:3.009ex;" alt="{\displaystyle {\tilde {D}}_{7}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineD7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">E7+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{7}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c251975c254e8e74513a013145d6ec2b0e5d016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{7}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:AffineE7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#ffffe0">E8 <a class="external text" href="https://commons.wikimedia.org/wiki/File:DynkinE8Full.svg%7C"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>9 </th> <td bgcolor="#e0ffe0">A7++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineA7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">B7++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineB7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">D7++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineD7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">E7++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:HyberbolicAffineE7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#ffe0e0">E9=E8+=<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {E}}_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {E}}_{8}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7960ec54a7dac08a847e38ee3137a3e95a9044" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.83ex; height:3.009ex;" alt="{\displaystyle {\tilde {E}}_{8}}" /> <a class="external text" href="https://commons.wikimedia.org/wiki/File:E9-AffineE8.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>10 </th> <td bgcolor="#e0e0ff">A7+++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineA7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/2/2e/Dyn-loop1.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/9/96/Dyn-3s.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/5/53/Dyn-nodes.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/e/e9/Dyn-loop2g.png" decoding="async" width="13" height="24" class="mw-file-element" data-file-width="13" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/b/b3/Dyn-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/1/17/Dyn-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0e0ff">B7+++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineB7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/4/48/Dyn2-4a.png" decoding="async" width="8" height="24" class="mw-file-element" data-file-width="8" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0e0ff">D7+++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineD7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0e0ff">E7+++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:VeryExtendedAffineE7.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td> <td bgcolor="#e0ffe0">E10=E8++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:E10-HyperbolicAffineE8.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>11 </th> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff"> </td> <td bgcolor="#e0e0ff">E11=E8+++ <a class="external text" href="https://commons.wikimedia.org/wiki/File:E11-VeryExtendedAffineE8.svg"> <img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/7/7b/Dyn2-branch.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/Dyn2-node.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/c/c8/Dyn2-3.png" decoding="async" width="6" height="24" class="mw-file-element" data-file-width="6" data-file-height="24" /><img src="//upload.wikimedia.org/wikipedia/commons/a/a5/Dyn2-nodeg.png" decoding="async" width="9" height="24" class="mw-file-element" data-file-width="9" data-file-height="24" /></a> </td></tr> <tr align="center"> <th>Det(Mn) </th> <td>8(8 − n) </td> <td>2(8 − n) </td> <td>4(8 − n) </td> <td>2(8 − n) </td> <td>9 − n </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=24" title="Edit section: See also">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style 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data-file-width="1024" data-file-height="1376" /></a></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Category:Dynkin_diagrams" class="extiw" title="commons:Category:Dynkin diagrams">Dynkin diagrams</a>.</div></div> </div> <ul><li><a href="/wiki/Satake_diagram" title="Satake diagram">Satake diagram</a></li> <li><a href="/wiki/List_of_irreducible_Tits_indices" title="List of irreducible Tits indices">List of irreducible Tits indices</a></li> <li><a href="https://en.wikibooks.org/wiki/de:Beweisarchiv:_Lie-Algebren:_Wurzelsysteme:_Klassifikation_von_Wurzelsystemen" class="extiw" title="wikibooks:de:Beweisarchiv: Lie-Algebren: Wurzelsysteme: Klassifikation von Wurzelsystemen">Klassifikation von Wurzelsystemen</a> (Classification of root systems) (in German)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=25" title="Edit section: Notes">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-4"><a href="#cite_ref-4">^</a> In this section we refer to the general class as "Coxeter diagrams" rather than "Coxeter–Dynkin diagrams" for clarity, as there is great potential for confusion, and for concision. </li> <li id="cite_note-13"><a href="#cite_ref-13">^</a> Note that Stekloshchik uses an arrow convention opposite to that of this article. </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Citations">Citations</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=26" title="Edit section: Citations">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <a href="#CITEREFHall2015">Hall 2015</a> Section 8.6 </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <a href="#CITEREFHall2015">Hall 2015</a> Propositions 8.6 and 8.13 </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <a href="#CITEREFHall2015">Hall 2015</a> Proposition 8.6 </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBaez1998" class="citation cs2">Baez, John (April 13, 1998), <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/week119.html">This Week's Finds in Mathematical Physics (Week 119)</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=This+Week%27s+Finds+in+Mathematical+Physics+%28Week+119%29&rft.date=1998-04-13&rft.aulast=Baez&rft.aufirst=John&rft_id=http%3A%2F%2Fmath.ucr.edu%2Fhome%2Fbaez%2Fweek119.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <a href="#CITEREFFultonHarris1991">Fulton & Harris 1991</a>, Proposition D.40 </li> <li id="cite_note-overout-7">^ <a href="#cite_ref-overout_7-0">a</a> <a href="#cite_ref-overout_7-1">b</a> <a href="#cite_ref-overout_7-2">c</a> <a rel="nofollow" class="external text" href="https://mathoverflow.net/q/14735">Outer automorphisms of simple Lie Algebras</a> </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <a href="#CITEREFHumphreys1972">Humphreys 1972</a>, § 16.5 </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> <a href="#CITEREFJacobson1971">Jacobson 1971</a>, § 7 </li> <li id="cite_note-10"><a href="#cite_ref-10">^</a> Algebraic geometry and number theory: in honor of Vladimir Drinfeld's 50th Birthday, edited by Victor Ginzburg, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gGUTVxVieRIC&pg=PA47">p. 47, section 3.6: Cluster folding</a> </li> <li id="cite_note-stembridge-11">^ <a href="#cite_ref-stembridge_11-0">a</a> <a href="#cite_ref-stembridge_11-1">b</a> <a rel="nofollow" class="external text" href="http://www.math.lsa.umich.edu/~jrs/papers/folding.ps.gz">Folding by Automorphisms</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304091644/http://www.math.lsa.umich.edu/~jrs/papers/folding.ps.gz">Archived</a> 2016-03-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, John Stembridge, 4pp., 79K, 20 August 2008, <a rel="nofollow" class="external text" href="http://www.math.lsa.umich.edu/~jrs/other.html">Other Articles by John Stembridge</a> </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> See <a href="#CITEREFStekolshchik2008">Stekolshchik 2008</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gtwR-rd4--UC&pg=PA102">p. 102</a>, remark 5.4 for illustrations of these foldings and references. </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFZuber1998" class="citation book cs1">Zuber, Jean-Bernard (1998). "Generalized Dynkin diagrams and root systems and their folding". In Kashiwara, M.; Matsuo, A.; Saito, K.; Satake, I. (eds.). Topological Field Theory, Primitive Forms and Related Topics. Progress in Mathematics. Vol. 160. pp. 28–30. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.3122">10.1.1.54.3122</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4612-0705-4_16">10.1007/978-1-4612-0705-4_16</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-6874-1" title="Special:BookSources/978-1-4612-6874-1"><bdi>978-1-4612-6874-1</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12429369">12429369</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Generalized+Dynkin+diagrams+and+root+systems+and+their+folding&rft.btitle=Topological+Field+Theory%2C+Primitive+Forms+and+Related+Topics&rft.series=Progress+in+Mathematics&rft.pages=%3Cspan+class%3D%22nowrap%22%3E28-%3C%2Fspan%3E30&rft.date=1998&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.54.3122%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A12429369%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-0705-4_16&rft.isbn=978-1-4612-6874-1&rft.aulast=Zuber&rft.aufirst=Jean-Bernard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-armstrong-15">^ <a href="#cite_ref-armstrong_15-0">a</a> <a href="#cite_ref-armstrong_15-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFArmstrong2010" class="citation web cs1">Armstrong, John (March 5, 2010). <a rel="nofollow" class="external text" href="http://unapologetic.wordpress.com/2010/03/05/transformations-of-dynkin-diagrams/">"Transformations of Dynkin Diagrams"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Transformations+of+Dynkin+Diagrams&rft.date=2010-03-05&rft.aulast=Armstrong&rft.aufirst=John&rft_id=http%3A%2F%2Funapologetic.wordpress.com%2F2010%2F03%2F05%2Ftransformations-of-dynkin-diagrams%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-knapp-16">^ <a href="#cite_ref-knapp_16-0">a</a> <a href="#cite_ref-knapp_16-1">b</a> <a href="#CITEREFKnapp2002">Knapp 2002</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U573NrppkA8C&lpg=PA758">p. 758</a> </li> <li id="cite_note-overdraw-17">^ <a href="#cite_ref-overdraw_17-0">a</a> <a href="#cite_ref-overdraw_17-1">b</a> <a href="#cite_ref-overdraw_17-2">c</a> <a rel="nofollow" class="external text" href="https://mathoverflow.net/a/20855">Why are the Dynkin diagrams E6, E7 and E8 always drawn the way they are drawn?</a> </li> <li id="cite_note-18"><a href="#cite_ref-18">^</a> Section 2.1 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFStekolshchik2005" class="citation arxiv cs1">Stekolshchik, Rafael (2005). "Notes on Coxeter Transformations and the McKay correspondence". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/math/0510216v1">math/0510216v1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Notes+on+Coxeter+Transformations+and+the+McKay+correspondence&rft.date=2005&rft_id=info%3Aarxiv%2Fmath%2F0510216v1&rft.aulast=Stekolshchik&rft.aufirst=Rafael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-19"><a href="#cite_ref-19">^</a> See for example <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHumphreys1990" class="citation book cs1">Humphreys, James E. (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ODfjmOeNLMUC&pg=PA96">"48. Fundamental domain § Affine reflection groups"</a>. Reflection Groups and Coxeter Groups. Cambridge University Press. p. 96. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-43613-7" title="Special:BookSources/978-0-521-43613-7"><bdi>978-0-521-43613-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=48.+Fundamental+domain+%C2%A7+Affine+reflection+groups&rft.btitle=Reflection+Groups+and+Coxeter+Groups&rft.pages=96&rft.pub=Cambridge+University+Press&rft.date=1990&rft.isbn=978-0-521-43613-7&rft.aulast=Humphreys&rft.aufirst=James+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DODfjmOeNLMUC%26pg%3DPA96&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-20"><a href="#cite_ref-20">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKac1990" class="citation book cs1"><a href="/wiki/Victor_Kac" title="Victor Kac">Kac, Victor G.</a> (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kuEjSb9teJwC&pg=PA53">"4. A Classification of Generalized Cartan Matrices"</a>. Infinite-Dimensional Lie Algebras. Cambridge University Press. pp. 53–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-46693-6" title="Special:BookSources/978-0-521-46693-6"><bdi>978-0-521-46693-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=4.+A+Classification+of+Generalized+Cartan+Matrices&rft.btitle=Infinite-Dimensional+Lie+Algebras&rft.pages=53-&rft.pub=Cambridge+University+Press&rft.date=1990&rft.isbn=978-0-521-46693-6&rft.aulast=Kac&rft.aufirst=Victor+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DkuEjSb9teJwC%26pg%3DPA53&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-21"><a href="#cite_ref-21">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCarboneChungCobbsMcRae2010" class="citation journal cs1">Carbone, Lisa; Chung, Sjuvon; Cobbs, Leigh; McRae, Robert; Nandi, Debajyoti; Naqvi, Yusra; Penta, Diego (2010). "Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits". Journal of Physics A: Mathematical and Theoretical. 43 (15): 155209. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1003.0564">1003.0564</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010JPhA...43o5209C">2010JPhA...43o5209C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1751-8113%2F43%2F15%2F155209">10.1088/1751-8113/43/15/155209</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16946456">16946456</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics+A%3A+Mathematical+and+Theoretical&rft.atitle=Classification+of+hyperbolic+Dynkin+diagrams%2C+root+lengths+and+Weyl+group+orbits&rft.volume=43&rft.issue=15&rft.pages=155209&rft.date=2010&rft_id=info%3Aarxiv%2F1003.0564&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16946456%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1751-8113%2F43%2F15%2F155209&rft_id=info%3Abibcode%2F2010JPhA...43o5209C&rft.aulast=Carbone&rft.aufirst=Lisa&rft.au=Chung%2C+Sjuvon&rft.au=Cobbs%2C+Leigh&rft.au=McRae%2C+Robert&rft.au=Nandi%2C+Debajyoti&rft.au=Naqvi%2C+Yusra&rft.au=Penta%2C+Diego&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> <li id="cite_note-22"><a href="#cite_ref-22">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEnglertHouartTaorminaWest2003" class="citation journal cs1">Englert, François; Houart, Laurent; <a href="/wiki/Anne_Taormina" title="Anne Taormina">Taormina, Anne</a>; West, Peter (2003). "The symmetry of M-theories". Journal of High Energy Physics. 2003 (9): 020. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0304206">hep-th/0304206</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003JHEP...09..020E">2003JHEP...09..020E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1126-6708%2F2003%2F09%2F020">10.1088/1126-6708/2003/09/020</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15680493">15680493</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+High+Energy+Physics&rft.atitle=The+symmetry+of+M-theories&rft.volume=2003&rft.issue=9&rft.pages=020&rft.date=2003&rft_id=info%3Aarxiv%2Fhep-th%2F0304206&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15680493%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1126-6708%2F2003%2F09%2F020&rft_id=info%3Abibcode%2F2003JHEP...09..020E&rft.aulast=Englert&rft.aufirst=Fran%C3%A7ois&rft.au=Houart%2C+Laurent&rft.au=Taormina%2C+Anne&rft.au=West%2C+Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=27" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDynkin1947" class="citation cs2 cs1-prop-foreign-lang-source"><a href="/wiki/Eugene_Dynkin" title="Eugene Dynkin">Dynkin, E. B.</a> (1947), "The structure of semi-simple algebras .", Uspekhi Mat. Nauk, N.S. (in Russian), 2 (4(20)): 59–127</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Uspekhi+Mat.+Nauk&rft.atitle=The+structure+of+semi-simple+algebras+.&rft.volume=2&rft.issue=4%2820%29&rft.pages=%3Cspan+class%3D%22nowrap%22%3E59-%3C%2Fspan%3E127&rft.date=1947&rft.aulast=Dynkin&rft.aufirst=E.+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBourbaki1968" class="citation cs2"><a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Bourbaki, Nicolas</a> (1968), "Chapters 4–6", Groupes et algebres de Lie, Paris: Hermann</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapters+4%E2%80%936&rft.btitle=Groupes+et+algebres+de+Lie&rft.place=Paris&rft.pub=Hermann&rft.date=1968&rft.aulast=Bourbaki&rft.aufirst=Nicolas&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJacobson1971" class="citation cs2"><a href="/wiki/Nathan_Jacobson" title="Nathan Jacobson">Jacobson, Nathan</a> (1971-06-01), Exceptional Lie Algebras, CRC Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8247-1326-3" title="Special:BookSources/978-0-8247-1326-3"><bdi>978-0-8247-1326-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Exceptional+Lie+Algebras&rft.pub=CRC+Press&rft.date=1971-06-01&rft.isbn=978-0-8247-1326-3&rft.aulast=Jacobson&rft.aufirst=Nathan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHumphreys1972" class="citation cs2">Humphreys, James E. 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A.; <a href="/wiki/Gary_Seitz" title="Gary Seitz">Seitz</a>, G. M.; Onishchik, A. L. (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=D9ZF5O_JH2gC">Selected papers of E. B. Dynkin with commentary</a>. Providence, R.I.: American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-1065-1" title="Special:BookSources/978-0-8218-1065-1"><bdi>978-0-8218-1065-1</bdi></a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1757976">1757976</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Selected+papers+of+E.+B.+Dynkin+with+commentary&rft.place=Providence%2C+R.I.&rft.pub=American+Mathematical+Society&rft.date=2000&rft.isbn=978-0-8218-1065-1&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1757976%23id-name%3DMR&rft.aulast=Dynkin&rft.aufirst=Eugene+B.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DD9ZF5O_JH2gC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADynkin+diagram" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Dynkin_diagram&action=edit&section=28" title="Edit section: External links">edit</a>]</div> <ul><li><a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/week230.html">John Baez on the ubiquity of Dynkin diagrams in mathematics</a></li> <li><a rel="nofollow" class="external text" href="http://lesha.goder.com/dynkin-diagrams.html">Web tool for making publication-quality Dynkin diagrams with labels (written in JavaScript)</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output 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