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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, such that the algebraic- and coalgebraic structure satisfy certain compatibility relations. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, that the multiplication and the unit of the algebra both be coalgebra morphisms. These statements are equivalent in that they are expressed by the same commutative diagrams. 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 wikiPageRevisionID "600675741".
- Bialgebra hasPhotoCollection Bialgebra.
- Bialgebra subject Category:Bialgebras.
- Bialgebra subject Category:Coalgebras.
- Bialgebra subject Category:Monoidal_categories.
- Bialgebra type Abstraction100002137.
- Bialgebra type Class107997703.
- Bialgebra type Collection107951464.
- Bialgebra type Group100031264.
- Bialgebra type MonoidalCategories.
- 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, such that the algebraic- and coalgebraic structure satisfy certain compatibility relations. Specifically, the comultiplication and the counit are both unital algebra homomorphisms, or equivalently, that the multiplication and the unit of the algebra both be coalgebra morphisms. These statements are equivalent in that they are expressed by the same commutative diagrams.".
- Bialgebra label "Bialgebra".
- Bialgebra label "Bialgebra".
- Bialgebra label "Bialgèbre".
- Bialgebra label "雙代數".
- Bialgebra sameAs Bialgebra.
- Bialgebra sameAs Bialgèbre.
- Bialgebra sameAs m.01t59s.
- Bialgebra sameAs Q494141.
- Bialgebra sameAs Q494141.
- Bialgebra sameAs Bialgebra.
- Bialgebra wasDerivedFrom Bialgebra?oldid=600675741.
- Bialgebra depiction Bialgebra2.svg.
- Bialgebra isPrimaryTopicOf Bialgebra.
