The Braiding Structure and Duality of the Category of Left–Left BiHom–Yetter–Drinfeld Modules

Ling Liu and Bingliang Shen
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Ling Liu: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Bingliang Shen: Zhejiang College, Shanghai University of Finance and Economics, Jinhua 321013, China

Mathematics, 2022, vol. 10, issue 4, 1-17

Abstract: Let ( H , μ H , Δ H , α H , β H , ψ H , ω H , S H ) be a BiHom–Hopf algebra. First, we provide a non-trivial example of a left–left BiHom–Yetter–Drinfeld module and show that the category H H BHYD is a braided monoidal category. We also study the connection between the category H H BHYD and the category H M of the left co-modules over a coquasitriangular BiHom–bialgebra ( H , σ ) . Secondly, we prove that the category of finitely generated projective left–left BiHom–Yetter–Drinfeld modules is closed for left and right duality.

Keywords: left–left BiHom–Yetter–Drinfeld module; (coquasitriangular) BiHom-bialgebra; braiding; duality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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