On the structure theorem and the Maschke type theorem of Doi Hom-Hopf modules

TL;DR

This paper establishes conditions under which the forgetful functor in Doi Hom-Hopf modules is separable, introduces a generalized notion of integrals, and explores their applications in the context of Hom-Hopf algebra structures.

Contribution

It provides necessary and sufficient conditions for separability of the forgetful functor and generalizes the concept of integrals in Hom-Hopf modules.

Findings

Characterization of separable functors in Hom-Hopf modules

Introduction of a generalized notion of integrals

Applications to Hom-Hopf algebra structures

Abstract

We give necessary and sufficient conditions for the functor that forgets the $(C, \gamma)$-coaction to be separable. This leads to a generalized notion of integrals. Finally, the applications of our results are considered.