Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras

Abstract

*Abstract:Let (H,α) be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules \begin{array}{l}H\\ H\end{array}HYD is isomorphic to the center of the category of left (H,α)-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.

Keywords

Monoidal Hom-Hopf algebra / Hom-Yetter-Drinfeld module / center construction / duality

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