BiHom-four-angle Hopf modules and BiHom-Yetter-Drinfel'd modules

2026/08/05 by Dongdong Yan, Xiaoqian Liu
Mathematics · #math.QA #msc:16T05 #msc:18M15 #msc:17A30

paper · pdf

24pages

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

In this paper, we introduce the notion of four-angle Hopf modules over a BiHom-Hopf algebra H. We show that the category _H^H\mathfrakM_H^H of BiHom-four-angle Hopf modules admits a strict monoidal category structure with respect to either the BiHom-tensor product ⊗_H or the BiHom-cotensor product \square_H as its monoidal product. We prove that the category YD_H^H(m,n,p,q) of BiHom-(m,n,p,q)-Yetter-Drinfel'd modules with parameters m,n,p,q∈ℤ forms a strict braided monoidal category equipped with a new monoidal product. Furthermore, we establish monoidal equivalences between the monoidal categories YD_H^H(m,n,p,q) and _H^H\mathfrakM_H^H, where _H^H\mathfrakM_H^H carries either ⊗_H or \square_H as its monoidal product. Finally, we construct braiding structures for the monoidal categories (_H^H\mathfrakM_H^H,⊗_H) and (_H^H\mathfrakM_H^H,\square_H).

Citations

• BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category
• Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids
• Four-angle Hopf modules for Hom-Hopf algebras
• BiHom-Novikov algebras and infinitesimal BiHom-bialgebras
• The construction and deformation of BiHom-Novikov agebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra
• Yetter-Drinfeld modules for Hom-bialgebras
• Monoidal Hom-Hopf algebras
• On hom-algebras with surjective twisting
• Hom-Algebras and Hom-Coalgebras
• Hopf Modules and Yetter - Drinfel′d Modules
• Quantum Groups
• Differential calculus on compact matrix pseudogroups (quantum groups)