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The braided monoidal structure on the category of Hom-type Doi-Hopf modules (1512.08587v1)

Published 29 Dec 2015 in math.RA

Abstract: Let $(H,\a_H)$ be a Hom-Hopf algebra, $(A,\a_A)$ a right $H$-comodule algebra and $(C,\a_C)$ a left $H$-module coalgebra. Then we have the category $_A\mathcal{M}(H)C$ of Hom-type Doi-Hopf modules. The aim of this paper is to make the category $_A\mathcal{M}(H)C$ into a braided monoidal category. Our construction unifies quasitriangular and coquasitriangular Hom-Hopf algebras and Hom-Yetter-Drinfeld modules. We study tensor identities for monoidal categories of Hom-type Doi-Hopf modules. Finally we show that the category $_A\mathcal{M}(H)C$ is isomorphic to $A#C*$-module category.

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