Yetter-Drinfel'd Hopf algebras over groups of prime order
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.
Keywords
Cite
@article{arxiv.math/9905191,
title = {Yetter-Drinfel'd Hopf algebras over groups of prime order},
author = {Yorck Sommerhaeuser},
journal= {arXiv preprint arXiv:math/9905191},
year = {2009}
}
Comments
152 pages, uses multind and ams packages. See also http://www.mathematik.uni-muenchen.de/~sommerh