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Cantor systems, piecewise translations and simple amenable groups

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Nicolas Monod
2013

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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https://infoscience.epfl.ch/entities/publication/a6eb8223-fbc7-4ba2-b455-66a39a2f5199

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