Induction for weak symplectic Banach manifolds
type: Item
instance of: scholarly article
title: Induction for weak symplectic Banach manifolds
zbMATH Open document ID: 1145.53061
author: Anatol Odzijewicz
author: T. S. Ratiu
published in: Journal of Geometry and Physics
publication date: 2008-06-25T00:00:00Z
review text: This paper extends the symplectic induction procedure to the case of weak symplectic Banach manifolds. On weak symplectic manifolds not all smooth functions admit a Hamiltonian vector field. The authors first introduce the Poisson subalgebra of smooth functions that admit Hamiltonian vector fields. The symplectic induction procedure on weak symplectic manifolds is then presented. The theory is finally applied to several examples of Banach manifolds, namely, the Banach Lie group of \(k\)-diagonal operators. Explicit formulas are also obtained.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 46T05
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 5292519
zbMATH Keywords: symplectic manifold
zbMATH Keywords: Banach space
zbMATH Keywords: Banach Lie-Poisson space
zbMATH Keywords: Hamiltonian vector field
MaRDI profile type: Publication
full work available at URL: j.geomphys.2008.01.003
OpenAlex ID: W2147012725
cites work: Q4174811
cites work: Q5655596
cites work: Pukanszky's condition and symplectic induction
cites work: The Toda lattice. II. Existence of integrals
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q4318503
cites work: Banach Lie-Poisson spaces and reduction
cites work: Induced and coinduced Banach Lie-Poisson spaces and integrability
cites work: Theory of operator algebras I.
cites work: A universal phase space for particles in Yang-Mills fields
cites work: Induced representations and induced Hamiltonian actions
DOI: 10.1016/J.GEOMPHYS.2008.01.003
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description: scientific article; zbMATH DE number 5292519