Some ribbon elements for the quasi-Hopf algebra Dω(H)

Abstract

We construct an explicit isomorphism between the quasitriangular quasi-Hopf algebra [Formula: see text] defined in [D. Bulacu and F. Panaite, A generalization of the quasi-Hopf algebra [Formula: see text], Commun. Algebra 26 (1998) 4125–4141] 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 [Formula: see text].