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

2015/12/29 by Lu, Daowei
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1512.08587

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 _AM(H)^C of Hom-type Doi-Hopf modules. The aim of this paper is to make the category _AM(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 _AM(H)^C is isomorphic to A#C^*-module category.

Related

• Braided monoidal categories and Doi Hopf modules for monoidal Hom-Hopf algebras
• Covariant Bimodules Over Monoidal Hom-Hopf Algebras
• Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras
• Four-angle Hopf modules for Hom-Hopf algebras
• Hopf-cyclic coefficients in the braided setting