Prime II₁ factors arising from actions of product groups

2019/04/14 by Daniel Drimbe, Drimbe, Daniel · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.DS #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.1904.06637

To appear in Journal of Functional Analysis

arxiv created 2019/10/23 · arxiv updated 2019/10/24

Abstract

We prove that any II₁ factor arising from a free ergodic probability measure preserving action Γ\curvearrowright X of a product Γ=Γ₁×…×Γ_n of icc hyperbolic, free product or wreath product groups is prime, provided Γ_i\curvearrowright X is ergodic, for any 1≤ i≤ n. We also completely classify all the tensor product decompositions of a II₁ factor associated to a free ergodic probability measure preserving action of a product of icc, hyperbolic, property (T) groups. As a consequence, we derive a unique prime factorization result for such II₁ factors. Finally, we obtain a unique prime factorization theorem for a large class of II₁ factors which have property Gamma.

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• Relative solidity results and their applications to computations of some II₁ factor invariants

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