Hopf modules and the double of a quasi-Hopf algebra
Authors:
Peter Schauenburg
Affiliation:
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
Abstract:
We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by Yetter-Drinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new construction of the Drinfeld double of a quasi-Hopf algebra, as proposed by Majid and constructed by Hausser and Nill.