In this paper we show that for every congruent monotileable amenable group and for every metrizable Choquet simplex , there exists a minimal -subshift, which is free on a full measure set, whose set of invariant probability measures is affine homeomorphic to . 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  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. 821–839DOI 10.4171/GGD/506