Actions symplectiques de groupes compacts. (Symplectic actions of compact groups)
type: Item
instance of: scholarly article
title: Actions symplectiques de groupes compacts. (Symplectic actions of compact groups)
zbMATH Open document ID: 1001.37041
DOI: 10.1023/A:1014253511289
author: Yves Benoist
published in: Geometriae Dedicata
publication date: 2002-05-30T00:00:00Z
review text: The article provides a thorough and rather systematic exposition of the theory of symplectic actions of compact connected groups; complete proofs of all preliminary classical prerequisities are presented. The main result reads that the intersection of the Weyl chamber with the image of the moment map is a closed convex polyhedron and this permits to describe all symplectic actions of a torus which have at least one coisotropic orbit: they are products of a Hamiltonian coisotropic action by an antihamiltonian one. The first chapter treats symplectic manifolds, especially several improvements to the Darboux normal form \(\sum dp^i\wedge dq^i\) are presented. The second chapter deals with symplectic actions, moment mappings, holonomy groups, Hamiltonian and anti-Hamiltonian actions. The third chapter investigates the Hamiltonian actions of a torus: the image of the moment map is a convex polyhedron whose vertices are the images of the fixed points. The concluding three chapters deal with the general case of symplectic actions of compact groups and the main results mentioned above.
reviewed by: Jan Chrastina
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 37J35
zbMATH DE Number: 1747816
zbMATH Keywords: symplectic action
zbMATH Keywords: moment map
zbMATH Keywords: compact Lie group
zbMATH Keywords: convexity
MaRDI profile type: Publication
full work available at URL: a:1014253511289
OpenAlex ID: W201303440
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description: scientific article; zbMATH DE number 1747816