Symplectic leaves in real Banach Lie-Poisson spaces

2004/03/22 by Daniel Beltiţă, Beltiţă, Daniel, Tudor S. Raţiu +2 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Holomorphic and Operator Theory #math.OA #math.SG #msc:22E65 #msc:46L30 #msc:47L20 #msc:53D17 #msc:58B12

paper · pdf · doi:10.48550/arxiv.math/0403345

24 pages; new examples added; to appear in Geom. Funct. Anal

arxiv created 2005/03/31 · arxiv updated 2009/12/01

Abstract

We present several large classes of real Banach Lie-Poisson spaces whose characteristic distributions are integrable, the integral manifolds being symplectic leaves just as in finite dimensions. We also investigate when these leaves are embedded submanifolds or when they have Kähler structures. Our results apply to the real Banach Lie-Poisson spaces provided by the self-adjoint parts of preduals of arbitrary W^*-algebras, as well as of certain operator ideals.

Cited by

• A note on precotangent bundles: the example of Grassmannians
• Banach Poisson-Lie groups, Lax equations and the AKS theorem in infinite dimensions

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