Separable functors for the category of Doi Hom-Hopf modules
Volume 143 / 2016
Colloquium Mathematicum 143 (2016), 23-37
MSC: Primary 16T05.
DOI: 10.4064/cm6382-12-2015
Published online: 3 December 2015
Abstract
Let $\widetilde{\mathscr{H}}(\mathscr{M}_k)(H)^{C}_{A}$ be the category of Doi Hom-Hopf modules, $\widetilde{\mathscr{H}}(\mathscr{M}_k)_{A}$ be the category of $A$-Hom-modules, and $F$ be the forgetful functor from $\widetilde{\mathscr{H}}(\mathscr{M}_k)(H)^{C}_{A}$ to $\widetilde{\mathscr{H}}(\mathscr{M}_k)_{A}$. The aim of this paper is to give a necessary and suffcient condition for $F$ to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.
