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Reduction of Poisson manifolds

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Abstract

Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, U.S.A.

    Jerrold E. Marsden

  2. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, U.S.A.

    Tudor Ratiu

Authors
  1. Jerrold E. Marsden
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  2. Tudor Ratiu
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Additional information

Research supported by DOE contract DE-AT03-85ER 12097.

Supported by an A. P. Sloan Foundation fellowship.

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Marsden, J.E., Ratiu, T. Reduction of Poisson manifolds. Lett Math Phys 11, 161–169 (1986). https://doi.org/10.1007/BF00398428

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  • DOI: https://doi.org/10.1007/BF00398428

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