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In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups are a special case. The algebra is named in honour of Siméon Denis Poisson.

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rdf:type	yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797 yago:WikicatAlgebras
rdfs:label	Poisson algebra (en) Álgebra de Poisson (es) Algèbre de Poisson (fr) 泊松代数 (zh)
rdfs:comment	En matemáticas, un álgebra de Poisson es un álgebra asociativa junto con un corchete de Lie que además satisface la regla de Leibniz, esto es, que el corchete es también una derivación. Las álgebras de Poisson aparecen de forma natural en la mecánica hamiltoniana, y son también de gran importancia en el estudio de los . Las variedades con una estructura de álgebra de Poisson se conocen como variedades de Poisson, de entre las cuales las variedades simplécticas y los son casos particulares. Estas álgebras llevan su nombre en honor de Siméon Denis Poisson. (es) In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups are a special case. The algebra is named in honour of Siméon Denis Poisson. (en) Une algèbre de Poisson est une algèbre associative sur laquelle est défini un crochet de Lie qui satisfait la règle de Leibniz. L'exemple le plus important en est donné par l'algèbre des fonctions lisses sur une variété de Poisson ou, plus particulièrement, sur une variété symplectique. Ces algèbres ont été nommées algèbres de Poisson en l'honneur de Siméon Denis Poisson. (fr) 数学中，泊松代数（Poisson algebra）是具有一个满足莱布尼兹法则的李括号之结合代数；即括号也是导子。泊松代数自然出现于哈密顿力学，也是量子群研究的中心。携有一个泊松代数的流形也叫做泊松流形，辛流形与是其特列。此代数的名字以西莫恩·德尼·泊松命名。 (zh)
dcterms:subject	Symplectic geometry Algebras
Wikipage page ID	345704 (xsd:integer)
Wikipage revision ID	1091228008 (xsd:integer)
Link from a Wikipage to another Wikipage	Product rule Symplectic geometry Vector space Vertex operator algebra Jacobi identity Lie derivative Algebras Mathematics Lie algebra Siméon Denis Poisson Smooth function Yvette Kosmann-Schwarzbach Derivation (abstract algebra) Symplectic manifold Field (mathematics) Direct sum Universal enveloping algebra Hamiltonian mechanics Hamiltonian vector field Bilinear map Disjoint union Associative algebra Manifold Poisson bracket Kontsevich quantization formula Moyal bracket Tensor algebra Quantum group Poisson manifold Poisson superalgebra Poisson–Lie group Antibracket algebra
sameAs	Poisson algebra Poisson algebra Poisson algebra Poisson algebra Poisson algebra Poisson algebra Poisson algebra
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Cite_book dbt:Industrial_and_applied_mathematics
author	Yvette Kosmann-Schwarzbach
id	p/p110170 (en)
title	Poisson algebra (en)
has abstract	En matemáticas, un álgebra de Poisson es un álgebra asociativa junto con un corchete de Lie que además satisface la regla de Leibniz, esto es, que el corchete es también una derivación. Las álgebras de Poisson aparecen de forma natural en la mecánica hamiltoniana, y son también de gran importancia en el estudio de los . Las variedades con una estructura de álgebra de Poisson se conocen como variedades de Poisson, de entre las cuales las variedades simplécticas y los son casos particulares. Estas álgebras llevan su nombre en honor de Siméon Denis Poisson. (es) In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups are a special case. The algebra is named in honour of Siméon Denis Poisson. (en) Une algèbre de Poisson est une algèbre associative sur laquelle est défini un crochet de Lie qui satisfait la règle de Leibniz. L'exemple le plus important en est donné par l'algèbre des fonctions lisses sur une variété de Poisson ou, plus particulièrement, sur une variété symplectique. Ces algèbres ont été nommées algèbres de Poisson en l'honneur de Siméon Denis Poisson. (fr) 数学中，泊松代数（Poisson algebra）是具有一个满足莱布尼兹法则的李括号之结合代数；即括号也是导子。泊松代数自然出现于哈密顿力学，也是量子群研究的中心。携有一个泊松代数的流形也叫做泊松流形，辛流形与是其特列。此代数的名字以西莫恩·德尼·泊松命名。 (zh)
gold:hypernym	Algebra
prov:wasDerivedFrom	wikipedia-en:Poisson_algebra?oldid=1091228008&ns=0
page length (characters) of wiki page	4916 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Poisson_algebra
is Link from a Wikipage to another Wikipage of	Canonical quantization List of algebras Argument shift method Lie algebra representation List of mathematical topics in classical mechanics Lie algebra Siméon Denis Poisson Non-associative algebra Gerstenhaber algebra Isaiah Kantor Kantor double Universal enveloping algebra Hamiltonian mechanics Jim Stasheff Poisson bracket Algebra (disambiguation) Kontsevich quantization formula List of things named after Siméon Denis Poisson Poisson manifold Poisson superalgebra Poisson supermanifold Poisson–Lie group Nambu mechanics Poisson ring

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