Separable Functors for the Category of Doi–Hopf Modules, Applications

Author： Caenepeel S.   Militaru G.   Ion B.   Zhu S.  

Publisher： Academic Press

ISSN： 0001-8708

Source： Advances in Mathematics, Vol.145, Iss.2, 1999-08, pp. : 239-290

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Abstract

We prove a Maschke type theorem for the category of Doi–Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the C-coaction to be separable. This leads to a generalized notion of integrals. Our results can be applied to obtain Maschke type theorems for Yetter–Drinfel'd modules, Long dimodules, and modules graded by G-sets. Existing Maschke type theorems due to Doi and the authors are recovered as special cases. Copyright 1999 Academic Press.

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