Banach Lie-Poisson Spaces and Reduction

Banach Lie-poisson Spaces and Reduction

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.

Lie - Poisson spaces and reduction

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 also given.

O ct 2 00 3 Extensions of Banach Lie - Poisson spaces

The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W -algebras is given particular attention. Semidirect products and the extension of the restricted Banach Lie-Poisson space by the Banach Lie-Poisson space of compact operators are given as examples.

Exponentiation of Operator Lie Algebras on Banach Spaces

Affine Lie–Poisson reduction, Yang–Mills magnetohydrodynamics, and superfluids

This paper develops the theory of affine Lie–Poisson reduction and applies this process to Yang–Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin–Noether circulation theorem is presented and is applied to these examples. PACS numbers: 02.20.Sv, 47....