# Some ribbon elements for the quasi-Hopf algebra $D^\omega(H)$

## TL;DR

This paper constructs explicit isomorphisms and ribbon elements for the quasi-Hopf algebra $D^omega(H)$, advancing the understanding of its structure and properties in quantum algebra.

## Contribution

It provides explicit isomorphisms and new characterizations for ribbon structures in quasi-Hopf algebras, specifically for $D^omega(H)$.

## Key findings

- Explicit isomorphism between $D^omega(H)$ and a quantum double quasi-Hopf algebra
- New characterizations for ribbon quasi-Hopf algebras
- Construction of ribbon elements for $D^omega(H)$

## Abstract

We construct an explicit isomorphism between the quasitriangular quasi-Hopf algebra $D^\omega(H)$ defined in \cite{bp} and a certain quantum double quasi-Hopf algebra. We give also new characterizations for a quasitriangular quasi-Hopf algebra to be ribbon and use them to construct some ribbon elements for $D^\omega(H)$.