Weak equivalence to Bernoulli shifts for some algebraic actions

2017/09/15 by Ben Hayes, Hayes, Ben · 1 citation
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1709.05372

openalex publication_date 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Namely, we prove that if G is a countable, discrete group and f∈ M_n(\Z(G)) is invertible on ℓ²(G)^{⊕ n}, but f is not invertible in M_n(\Z(G)), then the measure-preserving action of G on X_f equipped with the Haar measure is weakly equivalent to a Bernoulli action. We shall in fact prove this weak equivalence in the case that f has a "formal inverse in ℓ²".

Cited by

• Infinitesimal containment and sparse factors of iid

Related

• Weak equivalence and non-classifiability of measure preserving actions
• Bernoulli actions are weakly contained in any free action
• Weak isomorphisms between Bernoulli shifts
• A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
• Harmonic Models and Bernoullicity