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Results tagged with hopf-algebras
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user 12858
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 $G$.
7
votes
An algebra map between Hopf algebras that does not commute with the counit
Such a map can certainly exist. For instance, take the $k$-algebra $G = k \times k$, with
$$ \begin{aligned}
&\Delta(1,0) = (1,0) \otimes (1,0) + (0,1) \otimes (0,1), \\
&\Delta(0,1) = (1,0) \otimes ( …
- 6,614
2
votes
Algebraic Groups, Modules, and Comodules
I think that Waterhouse's "Introduction to Affine Group Schemes" (1979), section 3.2 "Comodules", might be what you're looking for.
I'm not sure why you have the constraint "non-zero characteristic" …
- 6,614