Brzeziński's Crossed Products and Braided Hopf Crossed Products

Abstract

Recently, we introduced a notion of braided Hopf crossed product which generalizes the notion of classical Hopf crossed product defined independently by Blattner, Cohen and Montgomery and by Doi and Takeuchi. A very much general concept of crossed product is indebted to Brzezinski. In this paper we give a suficient condition for a Brzeziński's crossed product be a braided Hopf crossed product. Majid prove that the quantum double of a quasitriangular Hopf algebra is isomorphic to a classical Hopf crossed product. As an application of our result we obtain a generalization of Majid´s Theorem.