Fusion rules for abelian extensions of Hopf algebras

Abstract

We investigate the representation theory and fusion rules of a class of cocentral abelian (quasi-)Hopf extensions of Hopf algebras which includes twisted (generalized) quantum doubles of finite groups, and a certain quasi-Hopf algebra of Schauenburg associated to group-theoretical fusion categories. We then present a nontrivial example with noncommutative fusion rules.