Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 1: 177 - 197

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

RESEARCH ARTICLE

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

  • Bingliang SHEN 1 ,
  • Ling LIU , 2
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  • 1. Shanghai University of Finance and Economics Zhejiang College, Jinhua 321013, China
  • 2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China

Received date: 24 Nov 2015

Accepted date: 12 Mar 2016

Published date: 01 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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 HH 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.

Key words： Monoidal Hom-Hopf algebra; Hom-Yetter-Drinfeld module; center construction; duality

Cite this article

Bingliang SHEN , Ling LIU . Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras[J]. Frontiers of Mathematics in China, 2017 , 12(1) : 177 -197 . DOI: 10.1007/s11464-016-0594-z

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