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| The quasitriangular structures of biproduct Hopf algebras |
| ZHAO Li-hui, ZHAO Wen-zheng |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China; Department of Mathematics, Henan Normal University, Xinxiang 453002, China |
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Abstract The construction of the biproduct of Hopf algebras, which consists of smash product and the dual notion of smash coproduct, was first formulated by Radford. In this paper we study the quasitriangular structures over biproduct Hopf algebras B*H. We show the necessary and sufficient conditions for biproduct Hopf algebras to be quasitriangular. For the case when they are, we determine completely the unique formula of the quasitriangular structures. And so we find a way to construct solutions of the Yang-Baxter equation over biproduct Hopf algebras in the sense of (Majid, 1990).
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Received: 09 June 2006
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