In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra...
12 KB (1,612 words) - 10:08, 11 April 2024
Tensor algebra (section Bialgebra)
does not make it a bialgebra, but does lead to the concept of a cofree coalgebra, and a more complicated one, which yields a bialgebra, and can be extended...
23 KB (4,160 words) - 15:09, 12 January 2024
In mathematics, a Lie bialgebra is the Lie-theoretic case of a bialgebra: it is a set with a Lie algebra and a Lie coalgebra structure which are compatible...
5 KB (953 words) - 01:25, 13 November 2023
coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antihomomorphism satisfying a certain...
35 KB (4,397 words) - 02:43, 12 April 2024
quasi-bialgebras are a generalization of bialgebras: they were first defined by the Ukrainian mathematician Vladimir Drinfeld in 1990. A quasi-bialgebra differs...
8 KB (1,449 words) - 01:54, 25 April 2024
Exterior algebra (section Bialgebra structure)
. The exterior algebra (as well as the symmetric algebra) inherits a bialgebra structure, and, indeed, a Hopf algebra structure, from the tensor algebra...
76 KB (12,094 words) - 12:20, 12 July 2024
Representation theory of Hopf algebras (redirect from Representation of a bialgebra)
satisfying these conditions. This is the motivation for the definition of a bialgebra, where Δ is called the comultiplication and ε is called the counit. In...
6 KB (1,180 words) - 00:11, 11 November 2019
operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...
20 KB (2,689 words) - 03:33, 28 July 2024
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...
7 KB (1,124 words) - 02:39, 10 December 2023
operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...
16 KB (2,813 words) - 08:33, 25 May 2024