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

Rufus Willett

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

Operator Algebras 2015-05-25 v2

Authors: Rufus Willett

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 \'{e}tale.

Keywords

c*-algebra topological groups c*-algebras

Cite

@article{arxiv.1504.05615,
  title  = {A non-amenable groupoid whose maximal and reduced $C^*$-algebras are the same},
  author = {Rufus Willett},
  journal= {arXiv preprint arXiv:1504.05615},
  year   = {2015}
}

Comments

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

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