New Braided T-Categories over Weak Crossed Hopf Group Coalgebras

Abstract EN

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 ???α(H) for α∈π and use it to construct a braided T-category ???(H).

As an application, we give the concept of a Long dimodule category H?ℒH for a weak crossed Hopf group coalgebra H with quasitriangular and coquasitriangular structures and obtain that H?ℒH is a braided T-category by translating it into a weak Yetter-Drinfel'd module subcategory ???(H⊗H).