Geodesic
A Maschke type theorem for relative Hom-Hopf modules
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 783-799.

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Let $(H,\alpha )$ be a monoidal Hom-Hopf algebra and $(A,\beta )$ a right $(H,\alpha )$-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 $(A, \beta )$-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 $(H, \alpha )$-coaction to be separable. This leads to a generalized notion of integrals.
DOI : 10.1007/s10587-014-0132-7
Classification : 16T05
Keywords: monoidal Hom-Hopf algebra; separable functors; Maschke type theorem; total integral; relative Hom-Hopf module 
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Guo, Shuangjian; Chen, Xiu-Li. A Maschke type theorem for relative Hom-Hopf modules. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 783-799. doi : 10.1007/s10587-014-0132-7. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0132-7/

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