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Yetter-Drinfel'd Hopf algebras over groups of prime order

Yorck Sommerhaeuser
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Abstract

We prove a structure theorem for Yetter-Drinfel'd Hopf algebras over groups of prime order that are nontrivial, cocommutative, and cosemisimple: Under certain assumptions on the base field, these algebras can be decomposed into a tensor product of the dual group ring of the group of prime order and an ordinary group ring of some other group. This tensor product is a crossed product as an algebra and an ordinary tensor product as a coalgebra. In particular, the dimension of such a Yetter-Drinfel'd Hopf algebra is divisible by the prime under consideration. We also find explicit examples of such Yetter-Drinfel'd Hopf algebras and apply the result to the classification program for semisimple Hopf algebras.

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Yorck Sommerhaeuser. 1999-05-30. Yetter-Drinfel'd Hopf algebras over groups of prime order. https://arxiv.org/abs/math/9905191

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