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

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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 H H H Y D 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.

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Authors and Affiliations

  1. Shanghai University of Finance and Economics Zhejiang College, Jinhua, 321013, China

    Bingliang Shen

  2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Ling Liu

Authors
  1. Bingliang Shen
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  2. Ling Liu
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Correspondence to Ling Liu.

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Shen, B., Liu, L. Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras. Front. Math. China 12, 177–197 (2017). https://doi.org/10.1007/s11464-016-0594-z

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  • DOI: https://doi.org/10.1007/s11464-016-0594-z

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