Hopf algebra deformations of binary polyhedral groups
Quantum Algebra
2010-11-25 v2 Rings and Algebras
Abstract
We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z_2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups and describe its category of representations. We also prove a strengthening of a result of Nichols and Richmond on cosemisimple Hopf algebras with a 2-dimensional irreducible comodule in the finite dimensional context. Finally, we give some applications to the classification of certain classes of semisimple Hopf algebras.
Cite
@article{arxiv.0907.1879,
title = {Hopf algebra deformations of binary polyhedral groups},
author = {Julien Bichon and Sonia Natale},
journal= {arXiv preprint arXiv:0907.1879},
year = {2010}
}
Comments
revised version. Corrected proof of Proposition 3.2, a few changes in Subsection 4.2