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Banach Lie-Poisson Spaces and Reduction

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Abstract

The category of Banach Lie-Poisson spaces is introduced and studied. It is shown that the category of W *-algebras can be considered as one of its subcategories. Examples and applications of Banach Lie-Poisson spaces to quantization and integration of Hamiltonian systems are given. The relationship between classical and quantum reduction is discussed.

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Authors and Affiliations

  1. Institute of Physics, University of Bialystok, Lipowa 41, 15424, Bialystok, Poland

    Anatol Odzijewicz

  2. Centre Bernoulli, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Tudor S. Ratiu

Authors
  1. Anatol Odzijewicz
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  2. Tudor S. Ratiu
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Correspondence to Tudor S. Ratiu.

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Communicated by L. Takhtajan

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Odzijewicz, A., Ratiu, T. Banach Lie-Poisson Spaces and Reduction. Commun. Math. Phys. 243, 1–54 (2003). https://doi.org/10.1007/s00220-003-0948-8

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