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.