Completely positive entropy actions of sofic groups with ℤ in their center

2015/09/06 by Peter Burton, Burton, Peter
Mathematics · #Mathematical Dynamics and Fractals #Advanced Operator Algebra Research #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1509.01861

Abstract

Let Γ be a sofic group with a copy of ℤ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving Γ actions with completely positive entropy, none of which is a factor of a Bernoulli shift. Our construction shows that the relation of isomorphism among completely positive entropy Γ actions is not smooth, in contrast with the relation of isomorphism among Bernoulli shifts.

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