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Semisimplicity of the categories of Yetter-Drinfeld modules and Long dimodules

S. Caenepeel·T. Guédénon
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Abstract

Let $k$ be a field, and $H$ a Hopf algebra with bijective antipode. If $H$ is commutative, noetherian, semisimple and cosemisimple, then the category ${}_{H}{\mathcal {YD}}^H$ of Yetter-Drinfeld modules is semisimple. We also prove a similar statement for the category of Long dimodules, without the assumption that $H$ is commutative.

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S. Caenepeel, T. Guédénon. 2002-10-30. Semisimplicity of the categories of Yetter-Drinfeld modules and Long dimodules. https://arxiv.org/abs/math/0210461

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