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- Lie_bialgebra abstract "In mathematics, a Lie bialgebra is the Lie-theoretic case of a bialgebra: it's a set with a Lie algebra and a Lie coalgebra structure which are compatible.It is a bialgebra where the comultiplication is skew-symmetric and satisfies a dual Jacobi identity, so that the dual vector space is a Lie algebra, whereas the comultiplication is a 1-cocycle, so that the multiplication and comultiplication are compatible. The cocycle condition implies that, in practice, one studies only classes of bialgebras that are cohomologous to a Lie bialgebra on a coboundary. They are also called Poisson-Hopf algebras, and are the Lie algebra of a Poisson-Lie group.Lie bialgebras occur naturally in the study of the Yang-Baxter equations.".
- Lie_bialgebra wikiPageID "4290894".
- Lie_bialgebra wikiPageLength "5228".
- Lie_bialgebra wikiPageOutDegree "21".
- Lie_bialgebra wikiPageRevisionID "651991483".
- Lie_bialgebra wikiPageWikiLink Bialgebra.
- Lie_bialgebra wikiPageWikiLink Category:Coalgebras.
- Lie_bialgebra wikiPageWikiLink Category:Lie_algebras.
- Lie_bialgebra wikiPageWikiLink Category:Symplectic_geometry.
- Lie_bialgebra wikiPageWikiLink Coalgebra.
- Lie_bialgebra wikiPageWikiLink Cocycle_(algebraic_topology).
- Lie_bialgebra wikiPageWikiLink Comultiplication.
- Lie_bialgebra wikiPageWikiLink Jacobi_identity.
- Lie_bialgebra wikiPageWikiLink Lie_algebra.
- Lie_bialgebra wikiPageWikiLink Lie_coalgebra.
- Lie_bialgebra wikiPageWikiLink Manin_triple.
- Lie_bialgebra wikiPageWikiLink Mathematics.
- Lie_bialgebra wikiPageWikiLink Poisson-Lie_group.
- Lie_bialgebra wikiPageWikiLink Poisson_bivector.
- Lie_bialgebra wikiPageWikiLink Poisson_bracket.
- Lie_bialgebra wikiPageWikiLink Poisson_manifold.
- Lie_bialgebra wikiPageWikiLink Poisson_structure.
- Lie_bialgebra wikiPageWikiLink Poisson–Lie_group.
- Lie_bialgebra wikiPageWikiLink Self-complementary_graph.
- Lie_bialgebra wikiPageWikiLink Yang-Baxter_equation.
- Lie_bialgebra wikiPageWikiLink Yang–Baxter_equation.
- Lie_bialgebra wikiPageWikiLinkText "Lie bialgebra".
- Lie_bialgebra hasPhotoCollection Lie_bialgebra.
- Lie_bialgebra subject Category:Coalgebras.
- Lie_bialgebra subject Category:Lie_algebras.
- Lie_bialgebra subject Category:Symplectic_geometry.
- Lie_bialgebra hypernym Case.
- Lie_bialgebra type Person.
- Lie_bialgebra type Algebra.
- Lie_bialgebra type Theory.
- Lie_bialgebra comment "In mathematics, a Lie bialgebra is the Lie-theoretic case of a bialgebra: it's a set with a Lie algebra and a Lie coalgebra structure which are compatible.It is a bialgebra where the comultiplication is skew-symmetric and satisfies a dual Jacobi identity, so that the dual vector space is a Lie algebra, whereas the comultiplication is a 1-cocycle, so that the multiplication and comultiplication are compatible.".
- Lie_bialgebra label "Lie bialgebra".
- Lie_bialgebra sameAs m.0bvdw1.
- Lie_bialgebra sameAs Lie_bicebri.
- Lie_bialgebra sameAs Q6543812.
- Lie_bialgebra sameAs Q6543812.
- Lie_bialgebra wasDerivedFrom Lie_bialgebra?oldid=651991483.
- Lie_bialgebra isPrimaryTopicOf Lie_bialgebra.