Radford's biproduct for quasi-Hopf algebras and bosonization

Abstract

Let B be a braided Hopf algebra (with bijective antipode) in the category of left Yetter-Drinfeld modules over a quasi-Hopf algebra H. As in the case of Hopf algebras (J. Algebra 92 (1985) 322) the smash product B#H defined in (Comm, Algebra 28(2) (2000) 631) and a kind of smash coproduct afford a quasi-Hopf algebra structure on B circle times H. Using this, we obtain the structure of quasi-Hopf algebras with a projection. Further we will use this biproduct to describe the Majid bosonization (J. Algebra 163 (1994) 165) for quasi-Hopf algebras. (C) 2002 Elsevier Science B.V. All rights reserved.