Simple Hopf algebras and deformations of finite groups

CÉSAR GALINDO Y SONIA NATALE

MATHEMATICAL RESEARCH LETTERS

International Press

Año: 2006

1073-2780

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 ofthis 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.