Yetter-Drinfeld modules for Hom-bialgebras

Abstract

The aim of this paper is to define and study Yetter-Drinfeld modules over Hom-bialgebras, a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism. Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation. The category ${}_H^H\mathcal{Y}D$ of Yetter-Drinfeld modules with bijective structure maps over a Hom-bialgebra H with bijective structure map can be organized, in two different ways, as a quasi-braided pre-tensor category. If H is quasitriangular (respectively coquasitriangular) the first (respectively second) quasi-braided pre-tensor category ${}_H^H\mathcal{Y}D$ contains, as a quasi-braided pre-tensor subcategory, the category of modules (respectively comodules) with bijective structure maps over H.

18 pages

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