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- W1937629247 abstract "Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$. However, we also construct $A$-modules which have finitely generated Tate cohomology. It turns out that if a module in a connected component of the stable Auslander-Reiten quiver associated to $A$ has finitely generated Tate cohomology, then so does every module in that component. We apply some of these finite generation results on Tate cohomology to an algebra defined by Radford and to the restricted universal enveloping algebra of $sl_2(k)$." @default.
- W1937629247 created "2016-06-24" @default.
- W1937629247 creator A5023792328 @default.
- W1937629247 date "2013-09-19" @default.
- W1937629247 modified "2023-09-27" @default.
- W1937629247 title "Finite generation of Tate cohomology of symmetric Hopf algebras" @default.
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