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 \cite{PS}.
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.