Factorizable quasi-Hopf algebras - applications

We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfield 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. (C) 2004 Published by Elsevier B.V.