Frobenius and Mashke type Theorems for Doi-Hopf modules and entwined modules revisited: a unified approach

摘要

We study when induction functors (and their adjoints) between categories ofDoi-Hopf modules and, more generally, entwined modules are separable, resp.Frobenius. We present a unified approach, leading to new proofs of old resultsby the authors, as well as to some new ones. Also our methods provide acategorical explanation for the relationship between separability and Frobeniusproperties.