Cantor systems, piecewise translations and simple amenable groups

2012/04/10 by Kate Juschenko, Juschenko, Kate, Nicolas Monod +1 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Quantum chaos and dynamical systems #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.1204.2132

openalex publication_date 2012/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.

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