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Invariant star-product on a Poisson-Lie group and h-deformation of the corresponding Lie algebra

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Abstract

In this paper we prove that a left-invariant star-product on a Poisson-Lie group leads to the quantum Lie algebra structure on the corresponding Lie algebra of the Lie group.

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References

  • Abe, E. (1980).Hopf Algebras, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D. (1978a). Deformation theory and quantization, I,Annals of Physics,111, 61.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D. (1978b). Deformation theory and quantization, II,Annals of Physics,110, 111.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Drinfeld, V. G. (1983a).Soviet Mathematics Doklady,27, 86.

    Google Scholar 

  • Drinfeld, V. G. (1983b). On constant quasiclassical solution of the QYBE,Soviet Mathematics Doklady,28, 667–671.

    MATH  Google Scholar 

  • Drinfeld, V. G. (1987). Quantum groups inProceedings International Conference of Mathematicians, Berkeley, 1986, AMS, Providence, Rhode Island.

    Google Scholar 

  • Gurevich, D. (1990). Equation de Yang-Baxter et quantification des cocycles.Comptes Rendus de l'Academic des Sciences Paris,1310, 845–848.

    MathSciNet  Google Scholar 

  • Gurevich, D. and Rubstov, V. (1990). Yang-Baxter and deformation of associative and Lie algebras algebras, inLectures Notes in Mathematics, Vol. 1510, Springer, Berlin, p. 47.

    Google Scholar 

  • Jimbo, M. (1985). Quantum R-matrix related to the toda system, an algebraic approach, inLecture Notes in Physics, Vol. 246, Springer, Berlin, pp. 335–360.

    Google Scholar 

  • Jimbo, M. (1989).International Journal of Modern Physics, A,4, 3759.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Lu, J.-H. and Weinstein, A. (1990).Journal of Differential Geometry,31, 501.

    MATH  MathSciNet  Google Scholar 

  • Manin, Yu. I. (1988).Quantum Groups and Non-commutative Geometry, Centre de Recherches Mathématiques, Montreal, Canada.

    MATH  Google Scholar 

  • Moreno, C., and Valero, L. (1992). Star-products and quantization of Poisson-Lie groups,Journal of Geometry, and Physics,9, 369–402.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Ohn, C. (1992).Lectures in Mathematical Physics, Vol. 25, Springer, Berlin, pp. 85–88.

    Google Scholar 

  • Semenov-Tian-Shansky, M. (1985).Publications RIMS, Kyoto,21, 1237.

    Article  MATH  MathSciNet  Google Scholar 

  • Takhtajan, L. (1989).Introduction to Quantum Groups and Integrable Models of Quantum Field Theories, Lecture Notes in Physics, Vol. 370, Springer, Berlin.

    Google Scholar 

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Mansour, M. Invariant star-product on a Poisson-Lie group and h-deformation of the corresponding Lie algebra. Int J Theor Phys 36, 3007–3014 (1997). https://doi.org/10.1007/BF02435723

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  • DOI: https://doi.org/10.1007/BF02435723

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