Simple Hopf algebras and deformations of finite groups

CÉSAR GALINDO Y SONIA NATALE

MATHEMATICAL RESEARCH LETTERS

Año: 2007 p. 943 - 954

1073-2780

We show that certain twisting deformations of a family of supersolvablegroups are simple as Hopf algebras. These groups are direct products of two generalizeddihedral groups. Examples of this construction arise in dimensions 60 and $p^2q^2$, forprime numbers $p$, $q$ with $q|p − 1$. We also show that certain twisting deformation of thesymmetric group is simple as a Hopf algebra. On the other hand, we prove that everytwisting deformation of a nilpotent group is semisolvable. We conclude that the notionsof simplicity and (semi)solvability of a semisimple Hopf algebra are not determined byits tensor category of representations.