A non-amenable groupoid whose maximal and reduced $C^*$-algebras are the same

By Rufus Willett. 2015

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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 \'{e}tale.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a1279f7b511bf69268007dc3468b2c4f658d3c15