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Results tagged with hopf-algebras
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user 41706
A Hopf algebra is a vector space $H$ over a field $k$ endowed with an associative product $\times:H\otimes_k H\to H$ and a coassociative coproduct $\Delta:H\to H\otimes_k H$ which is a morphism of algebras. Unit $1:k\to H$, counit $\epsilon:H\to k$ and antipode $S:H\to H$ are also required. Such a structure exists on the group algebra $k G$ of a finite group $G$.
4
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Bialgebras with rigid representation theory
Repost from math.SE since no answer after two months, but feel free to close if not appropriate:
Everything is finite-dimensional over a field $k$.
Let $B$ be a bialgebra with $B\text{-mod}$ its cate …
- 338
4
votes
0
answers
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Categorical interpretation of the comodulus of a Hopf algebra?
Let $H$ be a finite-dimensional Hopf algebra.
Then it has a right cointegral $\lambda \in H^*$ and a left integral $c \in H$, characterized uniquely (up to scalar) by
\begin{align}
(\lambda \otime …
- 338