Groups admitting ergodic actions with generalized discrete spectrum
type: Item
instance of: scholarly article
title: Groups admitting ergodic actions with generalized discrete spectrum
zbMATH Open document ID: 0399.22005
DOI: 10.1007/BF01390227
author: Calvin C. Moore
author: Robert J. Zimmer
published in: Inventiones Mathematicae
publication date: 1979-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/142628
review text: The class of groups admitting an effective ergodic action with generalized discrete spectrum is a natural generalization of the class of maximally almost periodic groups. H. Freudenthal has given a complete characterization of the connected maximally almost periodic groups, and here we give a complete characterization of the almost connected groups admitting an effective ergodic action with generalized discrete spectrum. Namely, we show that an almost connected group is in this class if and only if it is type R. It is known that this is equivalent to the group being of polynomial growth, and for Lie groups is just the condition that all eigenvalues of the adjoint representation lie on the unit circle.
Mathematics Subject Classification ID: 22D40
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 3620176
zbMATH Keywords: generalization of class of maximally almost periodic groups
zbMATH Keywords: complete characterization of almost connected groups
MaRDI profile type: Publication
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OpenAlex ID: W2040272092
description: scientific article; zbMATH DE number 3620176