A Maschke type theorem for relative Hom-Hopf modules

TL;DR

This paper establishes a Maschke type theorem for relative Hom-Hopf modules, providing conditions for the separability of the forgetful functor and introducing a generalized concept of integrals.

Contribution

It extends Maschke's theorem to the setting of relative Hom-Hopf modules and characterizes the separability of the coaction forgetful functor.

Findings

Necessary and sufficient conditions for functor separability

Generalized notion of integrals in Hom-Hopf modules

Extension of classical Maschke theorem to Hom-Hopf setting

Abstract

In this paper, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the $(H, \a)$-coaction to be separable. This leads to a generalized notion of integrals.