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arXiv · 1207.2540

The equivalence relations of local homeomorphisms and Fell algebras

Lisa Orloff Clark·Astrid an Huef·Iain Raeburn
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Abstract

We study the groupoid C*-algebras associated to the equivalence relation induced by a quotient map on a locally compact Hausdorff space. This C*-algebra is always a Fell algebra, and if the quotient space is Hausdorff, it is a continuous-trace algebra. We show that the C*-algebra of a locally compact, Hausdorff and principal groupoid is a Fell algebra if and only if the groupoid is one of these relations, extending a theorem of Archbold and Somerset about etale groupoids. The C*-algebras of these relations are, up to Morita equivalence, precisely the Fell algebras with trivial Dixmier-Douady invariant as recently defined by an Huef, Kumjian and Sims. We use twisted groupoid algebras to provide examples of Fell algebras with non-trivial Dixmier-Douady invariant.

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Lisa Orloff Clark, Astrid an Huef, Iain Raeburn. 2012-07-11. The equivalence relations of local homeomorphisms and Fell algebras. https://arxiv.org/abs/1207.2540

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