Journal of Zhejiang University SCIENCE A
ISSN 1009-3095(Print), 1862-1775(Online), Monthly

2007   Vol. 8   No. 1   p. 149~157

On-line Access Date:   Dec. 18, 2006
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The quasitriangular structures of biproduct Hopf algebras

ZHAO Li-hui†1, ZHAO Wen-zheng2

(1Department of Mathematics, Zhejiang University, Hangzhou 310027, China)
(2Department of Mathematics, Henan Normal University, Xinxiang 453002, China)
†E-mail: lihuizhaos@126.com
Received June 9, 2006 revision accepted Sept. 14, 2006

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).

Key words: Hopf algebra, Quasitriangular structure, Biproduct
doi:10.1631/jzus.2007.A0149             CLC number: O153.3

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