36 Pages

Separable Functors for the Category of Doi–Hopf Modules II

WithStefaan Caenepeel, Bogdan Ion, Gigel Militaru, Shenglin Zhu

We give necessary and sufficient conditions for an induction functor (and its adjoint) between categories of Doi‐Hopf modules to be separable. As a consequence, we find new versions of Maschke’s Theorem, and we re‐cover some existing ones. In paiticular, we apply our results to the functor forgetting the action, and to Hopf Galois extensions.