A non-amenable groupoid whose maximal and reduced $C^{\ast }$-algebras are the same

Abstract

We construct a locally compact groupoid with the properties in the title. Our example is based closely on constructions used by Higson, Lafforgue, and Skandalis in their work on counterexamples to the Baum-Connes conjecture. It is a bundle of countable groups over the one point compactification of the natural numbers, and is Hausdorff, second countable and étale.

Version two has some clarifications, minor fixes, and additional background and references

References in corpus (1)

• A characterization of amenability of group actions on $C^{\ast }$-algebras