| The quasitriangular structures of biproduct Hopf algebras |
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| 作者姓名： | ZHAO Li-hui ZHAO Wen-zheng |
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| 作者单位： | ZHAO Li-hui1，ZHAO Wen-zheng2 (1Department of Mathematics，Zhejiang University，Hangzhou 310027，China) (2Department of Mathematics，Henan Normal University，Xinxiang 453002，China) |
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| 摘 要： | PRELIMINARIES The smash product and the smash coproduct are well known in the context of Hopf algebra (Molnar, 1979; Montgomery, 1993) and remain an active area of study (Zhao et al., 2000; Delvaux, 2004; Zhao and Wang, 2005). Let H be a Hopf algebra over a field k and suppose B is a left H-module algebra and is also a left H-comodule coalgebra. Radford (1985) found necessary and sufficient conditions for the smash product and the smash coproduct on B?H to make it a Hopf algebra, w…
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| 关 键 词： | 霍普夫代数 准三角结构 双积 压挤乘积 |
| 收稿时间： | 2006-06-09 |
| 修稿时间： | 2006-08-14 |
The quasitriangular structures of biproduct Hopf algebras |
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| ZHAO Li-hui ZHAO Wen-zheng.The quasitriangular structures of biproduct Hopf algebras[J].Journal of Zhejiang University Science,2007,8(1):149-157. |
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| Authors: | Li-hui Zhao Wen-zheng Zhao |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China;(2) 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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| Keywords: | Hopf algebra Quasitriangular structure Biproduct |
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