Some remarks about the weak containment property for groupoids and semigroups
Operator Algebras
2021-03-16 v5 Group Theory
Abstract
A locally compact groupoid is said to have the weak containment property if its full -algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for transformation groupoids relative to actions of exact discrete groups. We believe that for general \'etale groupoids one should have the same equivalence of the two properties under some mild exactness assumption. In this paper we try to support this statement.
Keywords
Cite
@article{arxiv.1604.01724,
title = {Some remarks about the weak containment property for groupoids and semigroups},
author = {Claire Anantharaman-Delaroche},
journal= {arXiv preprint arXiv:1604.01724},
year = {2021}
}
Comments
Compared to the first version, a false statement and its consequences have been removed