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

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

2002-10-30

arxiv.org/abs/math/0210461v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

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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