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- Bialgebra abstract "In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a coalgebra. The algebraic and coalgebraic structures are made compatible with a few more axioms. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms. (These statements are equivalent since they are expressed by the same commutative diagrams.)Similar bialgebras are related by bialgebra homomorphisms. A bialgebra homomorphism is a linear map that is both an algebra and a coalgebra homomorphism.As reflected in the symmetry of the commutative diagrams, the definition of bialgebra is self-dual, so if one can define a dual of B (which is always possible if B is finite-dimensional), then it is automatically a bialgebra.".
- Bialgebra thumbnail Bialgebra2.svg?width=300.
- Bialgebra wikiPageID "310887".
- Bialgebra wikiPageLength "9845".
- Bialgebra wikiPageOutDegree "45".
- Bialgebra wikiPageRevisionID "648204241".
- Bialgebra wikiPageWikiLink Algebra_over_a_field.
- Bialgebra wikiPageWikiLink Associative_algebra.
- Bialgebra wikiPageWikiLink Category:Bialgebras.
- Bialgebra wikiPageWikiLink Category:Coalgebras.
- Bialgebra wikiPageWikiLink Category:Monoidal_categories.
- Bialgebra wikiPageWikiLink Coalgebra.
- Bialgebra wikiPageWikiLink Commutative_diagram.
- Bialgebra wikiPageWikiLink Comultiplication.
- Bialgebra wikiPageWikiLink Convolution.
- Bialgebra wikiPageWikiLink Counit.
- Bialgebra wikiPageWikiLink Dual_(category_theory).
- Bialgebra wikiPageWikiLink Dual_space.
- Bialgebra wikiPageWikiLink Field_(mathematics).
- Bialgebra wikiPageWikiLink Frobenius_algebra.
- Bialgebra wikiPageWikiLink Group_(mathematics).
- Bialgebra wikiPageWikiLink Homomorphism.
- Bialgebra wikiPageWikiLink Homomorphisms.
- Bialgebra wikiPageWikiLink Hopf_algebra.
- Bialgebra wikiPageWikiLink Lie_bialgebra.
- Bialgebra wikiPageWikiLink Linear_map.
- Bialgebra wikiPageWikiLink Marginal_distribution.
- Bialgebra wikiPageWikiLink Mathematics.
- Bialgebra wikiPageWikiLink Multilinear_map.
- Bialgebra wikiPageWikiLink Probability_distribution.
- Bialgebra wikiPageWikiLink Quasi-bialgebra.
- Bialgebra wikiPageWikiLink Random_variable.
- Bialgebra wikiPageWikiLink Unital_algebra.
- Bialgebra wikiPageWikiLink Vector_space.
- Bialgebra wikiPageWikiLink File:Bialgebra1.svg.
- Bialgebra wikiPageWikiLink File:Bialgebra2.svg.
- Bialgebra wikiPageWikiLink File:Bialgebra3.svg.
- Bialgebra wikiPageWikiLink File:Bialgebra4a.svg.
- Bialgebra wikiPageWikiLink File:Coalg.png.
- Bialgebra wikiPageWikiLinkText "Bialgebra".
- Bialgebra wikiPageWikiLinkText "bialgebra".
- Bialgebra hasPhotoCollection Bialgebra.
- Bialgebra wikiPageUsesTemplate Template:Algebraic_structures.
- Bialgebra wikiPageUsesTemplate Template:Citation.
- Bialgebra wikiPageUsesTemplate Template:Refimprove.
- Bialgebra subject Category:Bialgebras.
- Bialgebra subject Category:Coalgebras.
- Bialgebra subject Category:Monoidal_categories.
- Bialgebra hypernym Space.
- Bialgebra type Article.
- Bialgebra type Algebra.
- Bialgebra type Article.
- Bialgebra type Theory.
- Bialgebra comment "In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a coalgebra. The algebraic and coalgebraic structures are made compatible with a few more axioms. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, the multiplication and the unit of the algebra both are coalgebra morphisms.".
- Bialgebra label "Bialgebra".
- Bialgebra sameAs Bialgebra.
- Bialgebra sameAs Bialgèbre.
- Bialgebra sameAs m.01t59s.
- Bialgebra sameAs Q494141.
- Bialgebra sameAs Q494141.
- Bialgebra sameAs 雙代數.
- Bialgebra wasDerivedFrom Bialgebra?oldid=648204241.
- Bialgebra depiction Bialgebra2.svg.
- Bialgebra isPrimaryTopicOf Bialgebra.