Compactness of minimal closed invariant sets of actions of unipotent groups
type: Item
instance of: scholarly article
title: Compactness of minimal closed invariant sets of actions of unipotent groups
zbMATH Open document ID: 0733.22005
DOI: 10.1007/BF00150402
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: Let G be a connected Lie group and \(\Gamma\) a lattice in G, i.e. a discrete subgroup with finite covolume. Let U be an Ad-unipotent subgroup of G, i.e. Ad u is a unipotent linear map for every \(u\in U\). The group U acts on G/\(\Gamma\) by left translations. A closed U-invariant subset \(X\subset G/\Gamma\) is called minimal if Ux is dense in X for every \(x\in X\). The author proves that every minimal closed U-invariant subset X of G/\(\Gamma\) is compact.
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 4212336
zbMATH Keywords: connected Lie group
zbMATH Keywords: lattice
zbMATH Keywords: discrete subgroup
zbMATH Keywords: unipotent subgroup
zbMATH Keywords: minimal closed U-invariant subset
author: Gregory Margulis
reviewed by: Herbert Abels
MaRDI profile type: Publication
cites work: On orbits of unipotent flows on homogeneous spaces
cites work: Q3735963
cites work: Values of quadratic forms at primitive integral points
cites work: Q3923256
full work available at URL: https://doi.org/10.1007/bf00150402
OpenAlex ID: W1999447013
description: scientific article; zbMATH DE number 4212336