Radford's biproduct for quasi-Hopf algebras and bosonization |
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Authors: | Daniel Bulacu Erna Nauwelaerts |
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Institution: | a Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109 Bucharest 1, Romania b Department of Mathematics, Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium |
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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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Keywords: | 57T05 81R05 81R50 |
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