Triangular Hopf algebras with the Chevalley property
Abstract
We say that a Hopf algebra has the Chevalley property if the tensor product of any two simple modules over this Hopf algebra is semisimple. In this paper we classify finite dimensional triangular Hopf algebras with the Chevalley property, over the field of complex numbers. Namely, we show that all of them are twists of triangular Hopf algebras with R-matrix having rank <=2, and explain that the latter ones are obtained from group algebras of finite supergroups by a simple modification procedure. We note that all examples of finite dimensional triangular Hopf algebras which are known to the authors, do have the Chevalley property, so one might expect that our classification potentially covers all finite dimensional triangular Hopf algebras.
Cite
@article{arxiv.math/0008232,
title = {Triangular Hopf algebras with the Chevalley property},
author = {Nicolas Andruskiewitsch and Pavel Etingof and Shlomo Gelaki},
journal= {arXiv preprint arXiv:math/0008232},
year = {2007}
}
Comments
26 pages, latex. The first proof of Theorem 5.2.1, which is given in Section 5, was completed. The original proof missed a step, and we are grateful to A. Davydov for pointing it out