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CLC number: O153.3

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Received: 2006-06-09

Revision Accepted: 2006-09-14

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.1 P.149-157

http://doi.org/10.1631/jzus.2007.A0149


The quasitriangular structures of biproduct Hopf algebras


Author(s):  ZHAO Li-hui, ZHAO Wen-zheng

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   lihuizhaos@126.com

Key Words:  Hopf algebra, Quasitriangular structure, Biproduct


ZHAO Li-hui, ZHAO Wen-zheng. The quasitriangular structures of biproduct Hopf algebras[J]. Journal of Zhejiang University Science A, 2007, 8(1): 149-157.

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author="ZHAO Li-hui, ZHAO Wen-zheng",
journal="Journal of Zhejiang University Science A",
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pages="149-157",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0149"
}

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%T The quasitriangular structures of biproduct Hopf algebras
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0149

TY - JOUR
T1 - The quasitriangular structures of biproduct Hopf algebras
A1 - ZHAO Li-hui
A1 - ZHAO Wen-zheng
J0 - Journal of Zhejiang University Science A
VL - 8
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SP - 149
EP - 157
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0149


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).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[2] Kassel, C., 1995. Quantum Groups, Graduate Texts in Mathematics. Springer-Verlag, New York, 155:172-177.

[3] Majid, S., 1990. Quasitriangular Hopf algebra and Yang-Baxter equations. Int. J. Modern Physics A, 5(1):1-91.

[4] Majid, S., 1994. Crossed products by braided groups and bosonization. J. Alg., 163(1):165-190.

[5] Molnar, R.K., 1977. Semi-direct products of Hopf algebras. J. Alg., 47(1):29-51.

[6] Montgomery, S., 1993. Hopf Algebras and Their Actions on Rings. CBMS Series in Math., Am. Math. Soc. Providence, 82:40-56.

[7] Radford, D.E., 1985. The structure of Hopf algebra with a projection. J. Alg., 92(2):322-347.

[8] Radford, D.E., 1992. On the antipode of quasitriangular Hopf algebra. J. Alg., 151(1):1-11.

[9] Sweedler, M.E., 1969. Hopf Algebras. Benjamin, New York, p.3-90.

[10] Zhao, W.Z., Wang, S.H., Jiao, Z.M., 1997. The twisted coproduct of the Hopf algebras and the HR Hopf algebras. Acta Mathematica Sinica, 40(4):591-596.

[11] Zhao, W.Z., Wang, S.H., Jiao, Z.M., 2000. On the quasitriangular structure of bicrossproduct Hopf algebra. Comm. Alg., 28:4839-4853.

[12] Zhao, W.Z., Wang, C.H., 2005. Weak Hopf algebra in Yetter-Drinfeld categories and weak biproducts. Northeast. Math. J., 21(4):492-502.

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