Cantor systems, piecewise translations and simple amenable groups

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.

The proof has been streamlined: the commutator of W(Z) is not needed anymore