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Separable functors for the category of Doi Hom-Hopf modules

Volume 143 / 2016

Shuangjian Guo, Xiaohui Zhang 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.

Authors

  • Shuangjian GuoSchool of Mathematics and Statistics
    Guizhou University of Finance and Economics
    Guiyang, 550025, P.R. China
    e-mail
  • Xiaohui ZhangSchool of Mathematical Sciences
    Qufu Normal University
    Qufu, Shandong 273165, P.R. China
    e-mail

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