Title :

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

Author(s) :

Beltiţă, Daniel [Auteur]
Ratiu, Tudor [Auteur]
Tumpach, Alice Barbara [Auteur]
Institut CNRS-PAULI [ICP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Functional Analysis

Pages :

138-168

Publisher :

Elsevier

Publication date :

2007-06

ISSN :

0022-1236

English keyword(s) :

Differential Geometry (math.DG)
Functional Analysis (math.FA)
FOS: Mathematics
Primary 46T05
Secondary 22E67
53D17
22E65

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We 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 ...
Show more >We 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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL