Invariant measures for actions of congruent monotileable amenable groups

  • Paulina Cecchi

    Universidad de Santiago de Chile, Chile
  • María Isabel Cortez

    Universidad de Santiago de Chile, Chile
Invariant measures for actions of congruent monotileable amenable groups cover
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Abstract

In this paper we show that for every congruent monotileable amenable group GG and for every metrizable Choquet simplex KK, there exists a minimal GG-subshift, which is free on a full measure set, whose set of invariant probability measures is affine homeomorphic to KK. 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 [3] for residually finite groups.

Cite this article

Paulina Cecchi, María Isabel Cortez, Invariant measures for actions of congruent monotileable amenable groups. Groups Geom. Dyn. 13 (2019), no. 3, pp. 821–839

DOI 10.4171/GGD/506