A new approach to the constructions of braided T-categories

Abstract

The aim of this paper is to construct a new braided T -category via the generalized Yetter-Drinfel'd modules and Drinfel'd codouble over Hopf algebra, an approach different from that proposed by Panaite and Staic [13]. Moreover, in the case of finite dimensional, we will show that this category coincides with the corepresentation of a certain coquasitriangular Turaev group algebra that we construct. Finally we apply our theory to the case of group algebra.

The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules

“…Since then their method was followed and generalized to other Hopf algebra structure, such as in [5] to weak Hopf algebra, in [16] to multiplier Hopf algebra, in [17] to monoidal Hom-Hopf algebra, in [4] to weak monoidal Hom-Hopf algebra and so on. And recently in [7] the first author constructed a braided T -category by a method dual to that of [8].…”