Abstract
Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Homcomodule 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, β)-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, α)-coaction to be separable. This leads to a generalized notion of integrals.
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The work was supported by the NSF of Jiangsu Province (No. BK2012736), the TianYuan Special Funds of the National Natural Science Foundation of China (No. 11426073), the Fund of Science and Technology Department of Guizhou Province (No. 2014GZ81365), Southeast University for Postdoctoral Innovation Funds (No. 3207013601) and Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1302019c).
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Guo, S., Chen, XL. A Maschke type theorem for relative Hom-Hopf modules. Czech Math J 64, 783–799 (2014). https://doi.org/10.1007/s10587-014-0132-7
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DOI: https://doi.org/10.1007/s10587-014-0132-7
Keywords
- monoidal Hom-Hopf algebra
- separable functors
- Maschke type theorem
- total integral
- relative Hom-Hopf module