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href="http://dbpedia.org/resource/Gerstenhaber_algebra">Gerstenhaber algebra</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/ontology/Building">building</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra. It is used in the Batalin–Vilkovisky formalism. It appears also in the generalization of Hamiltonian formalism known as the De Donder–Weyl theory as the algebra of generalized Poisson brackets defined on differential forms. </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Gerstenhaber.jpg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li>In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra. It is used in the Batalin–Vilkovisky formalism. It appears also in the generalization of Hamiltonian formalism known as the De Donder–Weyl theory as the algebra of generalized Poisson brackets defined on differential forms. (en)</li> <li style="display:none;">En mathématiques, une algèbre de Gerstenhaber est une structure algébrique qui généralise en un certain sens les algèbres de Lie et de Poisson. Elle tient son nom de Murray Gerstenhaber qui les a introduites en 1963. Formellement, c'est un espace vectoriel gradué muni de deux lois de degrés différents et de symétries opposées. Les algèbres de Gerstenhaber exactes, aussi connues sous le nom d’algèbres de Batalin-Vilkovisky ou BV-algèbres interviennent dans le (en) qui permet d'étudier les (en) des théories de jauges lagrangiennes. (fr)</li> <li style="display:none;">추상대수학과 대수적 위상수학 및 양자장론에서 거스틴해버 대수(영어: Gerstenhaber algebra)는 결합 법칙을 만족시키는 대수와 리 대수의 구조를 합친 대수 구조의 하나이다. (ko)</li> <li style="display:none;">格爾斯滕哈伯代数是Gerstenhaber在研究结合代数的形变时发现的。一个结合代数的形变跟它的有密切的关系，Gerstenhaber证明，Hochschild上复形实际上形成一个微分分次李代数，并且这个微分分次李代数完全控制了该结合代数的形变。Gerstenhaber的研究受到小平邦彦（Kodaira）-Spencer关于流形复结构形变研究的启发，这些思想后来由Deligne和Kontsevich等人加以系统完成。在下面后4个例子中，例2和例3是1990年代之前发现的，1993年，Deligne在给一些数学家的通信中猜测它们之间也许是有关系的，用数学语言表述，即：对任何一个结合代数，其Hochschild上复形是little disks operad的链(chain) operad上的代数。这就是著名的，最后由Kontsevich-Soibelman，McClure-Smith，Tamarkin和Voronov等人解决。Deligne猜想的证明涉及到了很多高深的数学工具，而这些工具都与拓扑共形场论有着密切的联系，因而引起了很多人的兴趣。稍后，在1997年，Chas和Sullivan的研究论文发表了名为弦拓扑的论文，发现了例5。他们的研究结果引起了数学家们很大的关注和进一步的研究，从而开辟了一门崭新的学科。最后，需要补充的是，关于Gerstenhaber代数的研究往往伴随着Batalin-Vilkovisky代数（简称）的研究。BV代数是一类特殊的Gerstenhaber代数，往往由Gerstenhaber代数里面的某种对称性而得到，如。 (zh)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail">dbo:thumbnail</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:thumbnail" 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href="http://purl.org/linguistics/gold/hypernym">gold:hypernym</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="gold:hypernym" resource="http://dbpedia.org/resource/Structure" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Structure">dbr:Structure</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type">rdf:type</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Abstraction100002137" href="http://dbpedia.org/class/yago/Abstraction100002137">yago:Abstraction100002137</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Algebra106012726" href="http://dbpedia.org/class/yago/Algebra106012726">yago:Algebra106012726</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Cognition100023271" href="http://dbpedia.org/class/yago/Cognition100023271">yago:Cognition100023271</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Content105809192" href="http://dbpedia.org/class/yago/Content105809192">yago:Content105809192</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Discipline105996646" href="http://dbpedia.org/class/yago/Discipline105996646">yago:Discipline105996646</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/KnowledgeDomain105999266" href="http://dbpedia.org/class/yago/KnowledgeDomain105999266">yago:KnowledgeDomain105999266</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Mathematics106000644" href="http://dbpedia.org/class/yago/Mathematics106000644">yago:Mathematics106000644</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/PsychologicalFeature100023100" href="http://dbpedia.org/class/yago/PsychologicalFeature100023100">yago:PsychologicalFeature100023100</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/PureMathematics106003682" href="http://dbpedia.org/class/yago/PureMathematics106003682">yago:PureMathematics106003682</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/ontology/Building" href="http://dbpedia.org/ontology/Building">dbo:Building</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Science105999797" href="http://dbpedia.org/class/yago/Science105999797">yago:Science105999797</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatAlgebras" href="http://dbpedia.org/class/yago/WikicatAlgebras">yago:WikicatAlgebras</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li>In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra. It is used in the Batalin–Vilkovisky formalism. It appears also in the generalization of Hamiltonian formalism known as the De Donder–Weyl theory as the algebra of generalized Poisson brackets defined on differential forms. (en)</li> <li style="display:none;">En mathématiques, une algèbre de Gerstenhaber est une structure algébrique qui généralise en un certain sens les algèbres de Lie et de Poisson. Elle tient son nom de Murray Gerstenhaber qui les a introduites en 1963. Formellement, c'est un espace vectoriel gradué muni de deux lois de degrés différents et de symétries opposées. Les algèbres de Gerstenhaber exactes, aussi connues sous le nom d’algèbres de Batalin-Vilkovisky ou BV-algèbres interviennent dans le (en) qui permet d'étudier les (en) des théories de jauges lagrangiennes. (fr)</li> <li style="display:none;">추상대수학과 대수적 위상수학 및 양자장론에서 거스틴해버 대수(영어: Gerstenhaber algebra)는 결합 법칙을 만족시키는 대수와 리 대수의 구조를 합친 대수 구조의 하나이다. (ko)</li> <li style="display:none;">格爾斯滕哈伯代数是Gerstenhaber在研究结合代数的形变时发现的。一个结合代数的形变跟它的有密切的关系，Gerstenhaber证明，Hochschild上复形实际上形成一个微分分次李代数，并且这个微分分次李代数完全控制了该结合代数的形变。Gerstenhaber的研究受到小平邦彦（Kodaira）-Spencer关于流形复结构形变研究的启发，这些思想后来由Deligne和Kontsevich等人加以系统完成。在下面后4个例子中，例2和例3是1990年代之前发现的，1993年，Deligne在给一些数学家的通信中猜测它们之间也许是有关系的，用数学语言表述，即：对任何一个结合代数，其Hochschild上复形是little disks operad的链(chain) operad上的代数。这就是著名的，最后由Kontsevich-Soibelman，McClure-Smith，Tamarkin和Voronov等人解决。Deligne猜想的证明涉及到了很多高深的数学工具，而这些工具都与拓扑共形场论有着密切的联系，因而引起了很多人的兴趣。稍后，在1997年，Chas和Sullivan的研究论文发表了名为弦拓扑的论文，发现了例5。他们的研究结果引起了数学家们很大的关注和进一步的研究，从而开辟了一门崭新的学科。 (zh)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li>Gerstenhaber algebra (en)</li> <li style="display:none;">Algèbre de Gerstenhaber (fr)</li> <li style="display:none;">거스틴해버 대수 (ko)</li> <li style="display:none;">格尔斯滕哈伯代数 (zh)</li> </ul></td></tr><tr class="even"><td 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