Q1085814
type: Item
instance of: scholarly article
title: Représentation coadjointe quotient et espaces homogènes de contact ou localement conformément symplectiques. (Quotient coadjoint representation and homogeneous contact or locally conformally symplectic spaces)
zbMATH Open document ID: 0608.53045
author: André Lichnerowicz
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1986-01-01T00:00:00Z
review text: The starting point of this paper is the dual space \({\mathcal G}^*\) of a real Lie algebra \({\mathcal G}\) of dimension n. \({\mathcal G}^*\) is equipped with a natural Poisson structure. A sphere \(S^{n-1}\) with a natural Jacobi structure is obtained as a quotient by the group of positive homotheties. The leaves of \(S^{n-1}\) are the orbits of the quotient coadjoint mapping. The notion of quotient coadjoint representation of a Lie algebra or of a convex Lie group is introduced. A systematic study of this representation leads to the notion of homogeneous contact spaces (of odd dimension) and of locally conformally symplectic homogeneous spaces (of even dimension). A homogeneous contact space is a covering of a leaf of \(S^{n-1}\), which in turn may be proper or improper. An improper homogeneous contact space admits a corresponding Pfaffian homogeneous space as a covering. The results for locally conformally symplectic homogeneous spaces are similar.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 3984062
zbMATH Keywords: real Lie algebra
zbMATH Keywords: Jacobi structure
zbMATH Keywords: homogeneous contact spaces
zbMATH Keywords: conformally symplectic homogeneous spaces
reviewed by: Zhongheng Guo
MaRDI profile type: Publication
label: Représentation coadjointe quotient et espaces homogènes de contact ou localement conformément symplectiques. (Quotient coadjoint representation and homogeneous contact or locally conformally symplectic spaces)
description: scientific article; zbMATH DE number 3984062