1512.08587Dec 29, 2015

The braided monoidal structure on the category of Hom-type Doi-Hopf modules

Daowei Lu

Abstract

Let (H,_H) be a Hom-Hopf algebra, (A,_A) a right $H$ -comodule algebra and (C,_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

Nearby in the stack

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_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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