Separable functors for the category of Doi-Hopf modules, applications

Abstract

We prove a Maschke type theorem for the category of Doi-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the C-coaction to be separable. This leads to a generalized notion of integrals. Our results can be applied to obtain Maschke type theorems for Yetter-Drinfel'd modules, Long dimodules, and modules graded by G-sets. Existing Maschke type theorems due to Doi and the authors are recovered as special cases. © 1999 Academic Press.