The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

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dc.creatorBeltita, Daniel
dc.creatorRatiu, Tudor S.
dc.creatorTumpach, Alice Barbara
dc.date2006-06-14
dc.date.accessioned2026-07-07T07:17:16Z
dc.date.available2026-07-07T07:17:16Z
dc.descriptionWe investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0606327
dc.identifierhttp://arxiv.org/abs/math/0606327
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113878
dc.subjectDifferential Geometry
dc.subjectFunctional Analysis
dc.subjectPrimary 46T05; Secondary 22E67;53D17;22E65
dc.titleThe restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits
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