Yetter-Drinfeld category for the quasi-Turaev group coalgebra

TL;DR

This paper constructs a new Turaev braided group category by developing the Yetter-Drinfeld modules over a quasi-Turaev group coalgebra and proving their categorical equivalence to the center of the representation category.

Contribution

It introduces the construction of Yetter-Drinfeld modules over quasi-Turaev group coalgebras and establishes their categorical isomorphism to the center of the representation category.

Findings

Established the isomorphism between the Yetter-Drinfeld category and the center of Rep(H)

Constructed a new Turaev braided group category

Extended the theory of Yetter-Drinfeld modules to quasi-Turaev group coalgebras

Abstract

Let $\pi$ be a group. The aim of this paper is to construct the category of Yetter-Drinfeld modules over the quasi-Turaev group coalgebra $H=(\{H_\a\}_{\a\in\pi},\Delta,\varepsilon,S,\Phi)$, and prove that this category is isomorphic to the center of the representation category of $H$. Therefore a new Turaev braided group category is constructed.