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arXiv · 1709.08183

Invariant measures for actions of congruent monotileable amenable groups

Paulina Cecchi·María Isabel Cortez
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Abstract

In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability measures is affine homeomorphic to $K$. If the group is virtually abelian, the subshift is free. Congruent monotileable amenable groups are a generalization of amenable residually finite groups. In particular, we show that this class contains all the infinite countable virtually nilpotent groups. This article is a generalization to congruent monotileable amenable groups of one of the principal results shown in \cite{CP} for residually finite groups.

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Paulina Cecchi, María Isabel Cortez. 2017-09-24. Invariant measures for actions of congruent monotileable amenable groups. https://arxiv.org/abs/1709.08183

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