A Maschke Type Theorem for Doi-Hopf $π$-Modules (Communications in Mathematical Research, 2021)
We prove a Maschke type theorem for Doi-Hopf $π$-modules. A sufficientcondition for having a Maschke type property is that there exists a suitable totalintegral map for the Doi-Hopf $π$-modules in question. The applications of the resultsare considered. Finally, As an application of the existence of total integral, we provethat $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.
Keywords: integral; Hopf $π$-coalgebra; Hopf algebra; Maschke type theorem.