Banach Lie-Poisson spaces and reduction

Details Banach Lie-Poisson spaces and reduction Banach Lie-Poisson spaces and reduction

2002-10-14

arxiv.org/abs/math/0210207v3

Mathematics

Symplectic Geometry

58 pages, to apear in Comm.Math.Phys

Scientific paper

10.1007/s00220-003-0948-8

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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