Banach Lie-Poisson spaces and reduction
classification
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math.FA
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banachlie-poissonspacescategoryreductionalgebrasapplicationsclassical
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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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