Convexity properties of the coadjoint action of non-compact Lie groups
type: Item
instance of: scholarly article
title: Convexity properties of the coadjoint action of non-compact Lie groups
zbMATH Open document ID: 0887.22024
published in: Mathematische Annalen
publication date: 1998-05-12T00:00:00Z
review text: We call a coadjoint orbit of a finite dimensional real Lie algebra \({\mathfrak g}\) admissible if it is closed and its convex hull contains no affine lines. In this paper we study the closure of the set \({\mathfrak g}^*_{\text{adm}}\) of admissible coadjoint orbits in the dual \({\mathfrak g}^*\) of the Lie algebra \({\mathfrak g}\). In particular, we classify all orbits in this set which turns out to be a finite union of closed convex cones and show that the convex hull of an admissible orbit is always closed. We also use the results on coadjoint orbits to derive a new conjugacy theorem on adjoint orbits lying in convex cones.
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1121715
zbMATH Keywords: coadjoint action
zbMATH Keywords: invariant cone
zbMATH Keywords: Hermitian Lie algebra
zbMATH Keywords: coadjoint orbit
zbMATH Keywords: Lie algebra
zbMATH Keywords: admissible orbit
zbMATH Keywords: convex cones
author: Karl-Hermann Neeb
reviewed by: Karl-Hermann Neeb
MaRDI profile type: Publication
Wikidata QID: Q115388972
full work available at URL: s002080050131
OpenAlex ID: W2040774785
DOI: 10.1007/S002080050131
description: scientific article; zbMATH DE number 1121715