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Reduced Poisson actions

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Abstract

A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie groupG on the quotient of a Poisson G-spaceP to be a Poisson action, where both the Poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of Poisson homogeneous spaces are proved to be equivalent.

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References

  1. Semenov-Tian-Shansky, M. A., Dressing transformations and Poisson group actions, Pub1. Res. Inst. Sci. Kyoto Univ., 1985, 21:1237.

    MathSciNet  Google Scholar 

  2. Lu, J. H., Weinstein, A., Poisson Lie Groups, dressing transformations, and the Bruhat decomposition, J. Diff. Geom., 1990, 31:501.

    MATH  MathSciNet  Google Scholar 

  3. Vaisman, I., Lectures on the Geometry of Poisson Manifolds, Basel:Birkhauser, 1994.

    MATH  Google Scholar 

  4. Drinfel'd, V. G., On Poisson homogeneous spaces of Poisson-Lie groups, Theo. Math. Phys., 1993, 95:524.

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu, Z. J., Weinstein, A., Xu, P., Dirac structures and Poisson homogeneous spaces, Comm. Math. Phys., 1998, 192: 121.

    Article  MATH  MathSciNet  Google Scholar 

  6. Weinstein, A., Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan, 1988, 40:705.

    Article  MATH  MathSciNet  Google Scholar 

  7. Zakrzwski, S., Poisson structures on Poincare group, Comm. Math. Phys., 1997, 185:285.

    Article  MathSciNet  Google Scholar 

  8. Weinstein, A., Some remarks on dressing transformations, J. Math. Fac. Sci. Univ. Tokyo, 1988, 36:163.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Peking University, 100871, Beijing, China

    Zhangju Liu & Qilin Yang

Authors
  1. Zhangju Liu
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  2. Qilin Yang
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Correspondence to Zhangju Liu.

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Liu, Z., Yang, Q. Reduced Poisson actions. Sci. China Ser. A-Math. 43, 1026–1034 (2000). https://doi.org/10.1007/BF02898236

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  • DOI: https://doi.org/10.1007/BF02898236

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