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

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 $A\#C^{\ast }$-module category.

References in corpus (2)

• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-quantum groups I: quasi-triangular Hom-bialgebras