Hopf algebra deformations of binary polyhedral groups

Date
Authors
Bichon, Julien
Natale, Sonia
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Comment: revised version. Corrected proof of Proposition 3.2, a few changes in Subsection 4.2
Keywords
Mathematics - Quantum Algebra, Mathematics - Rings and Algebras, 16T05
Citation
Collections