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A Maschke type theorem for relative Hom-Hopf modules

Shuangjian Guo; Xiu-Li Chen — 2014

Czechoslovak Mathematical Journal

Let $(H, α)$ be a monoidal Hom-Hopf algebra and $(A, β)$ a right $(H, α)$ -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor $F$ from the category of relative Hom-Hopf modules to the category of right $(A, β)$ -Hom-modules has a right adjoint. Furthermore, 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 $(H, α)$ -coaction to be separable. This leads to a generalized...

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