Nichols algebras over groups with finite root system of rank two II
Quantum Algebra
2014-11-14 v3 Rings and Algebras
Abstract
We classify all non-abelian groups G such that there exists a pair (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).
Keywords
Cite
@article{arxiv.1302.0213,
title = {Nichols algebras over groups with finite root system of rank two II},
author = {I. Heckenberger and L. Vendramin},
journal= {arXiv preprint arXiv:1302.0213},
year = {2014}
}
Comments
21 pages. Final version. Accepted for publication in Journal of Group Theory