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Pairing and Quantum Double of Finite Hopf C~*-Algebras 被引量：1

Pairing and Quantum Double of Finite Hopf C~*-Algebras
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摘要 This paper defines a pairing of two finite Hopf C^＊-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^＊-algebra D（A, B）. The canonical embedding maps of A and B into the double are both isometric. This paper defines a pairing of two finite Hopf C^＊-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^＊-algebra D（A, B）. The canonical embedding maps of A and B into the double are both isometric.
作者 Ming LIU Li Ning JIANG Guo Sheng ZHANG
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第6期1121-1128,共8页 数学学报（英文版）
基金 the National Natural Science Foundation of China(No.10301004) Excellent Young Scholars Research Fund of Beijing Institute of Technology(00Y07-25)
关键词 Hopf C^＊-algebra PAIRING quantum double GNS representation Hopf C^＊-algebra, pairing, quantum double, GNS representation
分类号 O17 [理学—基础数学]
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参考文献17

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  • 2Kassel, C.: Quantum groups, Springer-Verlag, NewYork, 1995.
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  • 4Woronowicz, S. L.: Compact matrix psedogroups. Comm. Math. Phys., 111, 613-665 (1987).
  • 5Vaes, S., Daele, A. V.: Hopf C^*-algebras. Proc. Land. Math. Soc., 82(3), 337-384 (2001).
  • 6Daele, A. V.: Dual pairs of Hopf^*-algebras. Bull London Math. Soc., 25, 209-220 (1993).
  • 7Jiang, L. N., Li, Z. Y.: Representation and Duality of finite Hopf C^*-algebra. Acta Mathematica Sinica, Chinese Series, 47(6), 1155-1160 (2005).
  • 8Daele, A. V.: The Haar measure on finite quantum groups. Proc. Amer. Math. Soc., 125, 3489-3500 (1997).
  • 9Delvaux, L., Daele, A. V.: The Drinfel'd double for group-cograded multiplier Hopf algebras, arXiv: math.QA/0404029.
  • 10Drabant, B., Daele, A.V.: Pairing and quantum double of multiplier Hopf algebras. Algebras Represet. Theory, 4, 109-132 (2001).

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Acta Mathematica Sinica,English Series
2007年 第6期

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