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

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 $D^\omega(H)$.