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bialgebra (Definition)

A bialgebra is a vector space that is both a unital algebra and a coalgebra, such that the comultiplication and counit are unital algebra homomorphisms.

A bialgebra homomorphism is a linear map that is both an algebra and a coalgebra homomorphism.




"bialgebra" is owned by mhale.
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See Also: Yetter-Drinfel'd module


Attachments:
monoid bialgebra (Example) by joking
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Cross-references: coalgebra homomorphism, linear map, homomorphisms, counit, comultiplication, coalgebra, algebra, unital, vector space, bialgebra
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This is version 3 of bialgebra, born on 2002-10-18, modified 2004-12-29.
Object id is 3523, canonical name is Bialgebra.
Accessed 4401 times total.

Classification:
AMS MSC16W30 (Associative rings and algebras :: Rings and algebras with additional structure :: Coalgebras, bialgebras, Hopf algebras ; rings, modules, etc. on which these act)

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