Open AccessSymmetries in Yetter-Drinfel’d-Long categories
Author(s) -
Dongdong Yan,
Shuanhong Wang
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2114879y
Subject(s) - mathematics , subcategory , hopf algebra , homogeneous space , pure mathematics , symmetry (geometry) , algebra over a field , geometry
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 the 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.