Factorizable quasi-Hopf algebras—applications

Abstract

We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double D( H) of any finite dimensional quasi-Hopf algebra H is factorizable, and we characterize D( H) when H itself is factorizable. Finally, we prove that any finite dimensional factorizable quasi-Hopf algebra is unimodular. In particular, we obtain that the Drinfeld double D( H) is a unimodular quasi-Hopf algebra.