Disjointness, divisibility, and quasi-simplicity of measure-preserving actions
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.
scientific article; zbMATH DE number 5161623