New Braided T-Categories over Weak Crossed Hopf Group Coalgebras - Xuan Zhou; Tao Yang (Abstract and Applied Analysis)
Let H be a weak crossed Hopf group coalgebra over group π; we first introduce a kind of new α-Yetter-Drinfel’d module categories 𝒲𝒴𝒟α(H) for α∈π and use it to construct a braided T-category 𝒲𝒴𝒟(H). As an application, we give the concept of a Long dimodule category H𝒲ℒH for a weak crossed Hopf group coalgebra H with quasitriangular and coquasitriangular structures and obtain that H𝒲ℒH is a braided T-category by translating it into a weak Yetter-Drinfel'd module subcategory 𝒲𝒴𝒟(H⊗H).