Hopf modules and the double of a quasi-Hopf algebra

Abstract

We give a different proof for a structure theorem of Hausser andNill on Hopf modules over quasi-Hopf algebras. We extend thestructure the- orem to a classification of two-sided two-cosidedHopf modules by Yetter- Drinfeld modules, which can be defined intwo rather different manners for the quasi-Hopf case. Thecategory equivalence between Hopf modules and Yetter-Drinfeldmodules leads to a new construction of the Drinfeld double of aquasi-Hopf algebra, as proposed by Majid and constructed byHausser and Nill.