Disjointness, divisibility, and quasi-simplicity of measure-preserving actions
type: Item
instance of: scholarly article
title: Disjointness, divisibility, and quasi-simplicity of measure-preserving actions
zbMATH Open document ID: 1118.37007
author: Valery Ryzhikov
author: Jean-Paul Thouvenot
publication date: 2007-06-05T00:00:00Z
review text: It is shown that for a quasi-simple action there are no nontrivial higher-order selfjoinings, which generalize several earlier results obtained by \textit{A. M. Vershik} [J. Sov. Math. 23, 2243--2266 (1983); translation in Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 72, 26--61 (1977; Zbl 0408.28014)] and \textit{V. V. Ryzhikov} [Sb. Math. 188, No. 2, 237--263 (1997); translation from Mat. Sb. 188, No. 2, 67--94 (1997; Zbl 0892.28010), J. Dyn. Control Syst. 3, No. 1, 111--127 (1997; Zbl 0995.37002)]. The authors establish also that a quasi-simple action is disjoint in the sense of Furstenberg from a Gaussian automorphism.
reviewed by: Michael L. Blank
Mathematics Subject Classification ID: 37A15
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 5161623
zbMATH Keywords: Gaussian automorphism
zbMATH Keywords: quasi-simple action
zbMATH Keywords: selfjoining
MaRDI profile type: Publication
full work available at URL: s10688-006-0038-8
OpenAlex ID: W2029091867
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DOI: 10.1007/S10688-006-0038-8
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 5161623