2019/12/25 by Dongdong Yan, Yan, Dongdong, Wang, Shuanhong
Mathematics · #16T05 #18W05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1912.11577
openalex publication_date 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a Hopf algebra and LR(H) the category of Yetter-Drinfel'd-Long bimodules over H. We first give sufficient and necessary conditions for LR(H) to be symmetry and pseudosymmetry, respectively. We then introduce the definition of u-condition in LR(H) and discuss the relation between the u-condition and the symmetry of LR(H). Finally, we show that LR(H) over a triangular (cotriangular, resp.) Hopf algebra contains a rich symmetric subcategory.