Minimality and unique ergodicity for subgroup actions
type: Item
instance of: scholarly article
title: Minimality and unique ergodicity for subgroup actions
zbMATH Open document ID: 0910.43010
author: Shahar Mozes
author: Barak Weiss
publication date: 1998-11-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75329
review text: In the paper the following theorem is proved: Let \(G\) be a reductive algebraic \(R\)-group with compact center and let \(H\) be an \(R\)-subgroup of \(G\). Let \(H\) and \(G\) denote \(H^0_R\) and \(G^0_R\) , respectively, and let \(\Gamma\) be a lattice in \(G\). If the action of \(H\) on \(G/\Gamma\) is minimal then it is uniquely ergodic.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 1227221
zbMATH Keywords: minimal action
zbMATH Keywords: uniquely ergodic
zbMATH Keywords: homogeneous space
zbMATH Keywords: reductive algebraic \(R\)-group
zbMATH Keywords: lattice
reviewed by: Kaarin Riives
MaRDI profile type: Publication
OpenAlex ID: W2322154931
cites work: On ergodic quasi-invariant measures of group automorphism
cites work: Q4880543
cites work: Q4274267
cites work: Q3952851
cites work: Q5671414
cites work: Measure rigidity for almost linear groups and its applications
cites work: Q5644192
cites work: On the space of ergodic invariant measures of unipotent flows
cites work: Cartan subgroups and lattices in semi-simple groups
cites work: Invariant measures and orbit closures for unipotent actions on homogeneous spaces
cites work: Minimal sets of homogeneous flows
cites work: Unique Ergodicity of Horospherical Flows
cites work: Finite dimensional representations and subgroup actions on homogeneous spaces
DOI: 10.5802/AIF.1665
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1227221