About: Poisson–Lie group

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In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of Lie groups. Many quantum groups are quantizations of the Poisson algebra of functions on a Poisson–Lie group.

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	Poisson–Lie group (en) 泊松李群 (zh)
rdfs:comment	In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of Lie groups. Many quantum groups are quantizations of the Poisson algebra of functions on a Poisson–Lie group. (en) 泊松李群 (Poisson-Lie group) 是一种几何结构，也是李群和泊松流形，而且两种结构自洽。它的李群直积是泊松映射。它是經典力學和泊松几何学的有力的例子，也是表示論研究对象之一。它在无穷小尺度的形式就是李双代数。 (zh)
dct:subject	Symplectic geometry Structures on manifolds Lie groups
Wikipage page ID	4257207 (xsd:integer)
Wikipage revision ID	1094061636 (xsd:integer)
Link from a Wikipage to another Wikipage	Symplectic geometry Vladimir Drinfeld Poisson algebra Lie bialgebra Lie coalgebra Lie group Lie group–Lie algebra correspondence Structures on manifolds Mathematics Equivalence of categories Lie groups Simply connected space Borel subgroup Solvable group Quantum group Poisson manifold Affine quantum group Poisson map Quantum affine algebras Comultiplication Positive roots Semisimple group
Link from a Wikipage to an external page	https://archive.org/details/guidetoquantumgr0000char
sameAs	Poisson–Lie group Poisson–Lie group Poisson–Lie group Poisson–Lie group
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist
has abstract	In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of Lie groups. Many quantum groups are quantizations of the Poisson algebra of functions on a Poisson–Lie group. (en) 泊松李群 (Poisson-Lie group) 是一种几何结构，也是李群和泊松流形，而且两种结构自洽。它的李群直积是泊松映射。它是經典力學和泊松几何学的有力的例子，也是表示論研究对象之一。它在无穷小尺度的形式就是李双代数。 (zh)
gold:hypernym	Manifold
prov:wasDerivedFrom	wikipedia-en:Poisson–Lie_group?oldid=1094061636&ns=0
page length (characters) of wiki page	7438 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Poisson–Lie_group
is Link from a Wikipage to another Wikipage of	Poisson algebra Lie bialgebra Toda lattice Wigner–Weyl transform Poisson-Lie bracket List of things named after Siméon Denis Poisson List of things named after Sophus Lie Quantum group Poisson manifold Moment map Poisson-Lie group Viktor Ginzburg Poisson Lie group Poisson–Lie bracket
is Wikipage redirect of	Poisson-Lie bracket Poisson-Lie group Poisson Lie group Poisson–Lie bracket
is foaf:primaryTopic of	wikipedia-en:Poisson–Lie_group

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