A Maschke type theorem for weak group entwined modules and applications |
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Authors: | Dingguo Wang Quanguo Chen |
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Institution: | 1. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P. R China 2. School of Mathematics and Statistics, Yili Normal University Yining, Xinjiang, 835000, P. R. China
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Abstract: | Let π be a discrete group. Given a weak π-entwining structure \({(A,C)_{\pi - \psi }}\) and α ∈ π, we give the necessary and sufficient conditions for the forgetful functor \({F^{(\alpha )}}\) from the category \(U_A^{\pi - C}(\psi )\) of right \({(A,C)_{\pi - \psi }}\) -modules to the category \({M_{{A_\alpha }}}\) of right \({A_\alpha }\) -modules to be separable. This leads to a generalized notion of integrals. The results are applied to weak Doi-Hopf π-modules and to weak entwining modules. |
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