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

作者：Liu, Ling; Shen, Bingliang^*

来源：Mathematics, 2022, 10(4): 621.

DOI：10.3390/math10040621

• left-left BiHom-Yetter-Drinfeld module
• (coquasitriangular) BiHom-bialgebra
• braiding
• duality

Let (H, mu(H), & UDelta;(H), alpha(H), beta(H), psi(H), omega(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 (HBHYD)-B-H is a braided monoidal category. We also study the connection between the category (HBHYD)-B-H and the category M-H of the left co-modules over a coquasitriangular BiHom-bialgebra (H,sigma). Secondly, we prove that the category of finitely generated projective left-left BiHom-Yetter-Drinfeld modules is closed for left and right duality.

• 单位
  浙江师范大学