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⊗ 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.
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