Covariant Bimodules Over Monoidal Hom-Hopf Algebras

Abstract

Covariant Hom-bimodules are introduced and the structure theory of them in the Hom-setting is studied in a detailed way. The category of bicovariant Hom-bimodules is proved to be a (pre)braided monoidal category and its structure theory is also provided in coordinate form. The notion of Hom-Yetter-Drinfel'd modules is presented and it is shown that the category of Hom-Yetter-Drinfel'd modules is a (pre)braided tensor category as well. As one of the main results, a (pre)braided monoidal equivalence between these tensor categories is verified, which extends the fundamental theorem of Hom-Hopf modules.

40 pages, errors and typos corrected. Structure theory of covariant Hom-bimodules in coordinate form added

References in corpus (3)

• Hom-algebras and homology
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-quantum groups III: Representations and module Hom-algebras

Cited by in corpus (1)

• Hom-entwining structures and Hom-Hopf-type modules