Simple Hopf algebras and deformations of finite groups


We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and $p^2q^2$, for prime numbers $p$,$q$ with $q|p−1$. We also show that certain twisting deformation of the symmetric group is simple as a Hopf algebra. On the other hand, we prove that every twisting deformation of a nilpotent group is semisolvable. We conclude that the notions of simplicity and (semi)solvability of a semisimple Hopf algebra are not determined by its tensor category of representations.

Math. Res. Lett. 14 (2007), no. 6, 943–954
César Galindo
Associate Professor of Mathematics

My research interests include representation theory, category theory and their applications to Mathematical-Physics.