A New approach to the construction of braided T-categories

TL;DR

This paper introduces a novel method for constructing braided T-categories using generalized Yetter-Drinfel'd modules and Drinfel'd codoubles, offering a different approach from previous methods and connecting to coquasitriangular Turaev group algebras.

Contribution

It presents a new construction of braided T-categories via generalized Yetter-Drinfel'd modules and Drinfel'd codoubles, and relates these to coquasitriangular Turaev group algebras.

Findings

Constructed a new braided T-category using generalized Yetter-Drinfel'd modules.

Showed equivalence with corepresentation of a coquasitriangular Turaev group algebra in finite dimensions.

Applied the theory to group algebras.

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.