 

Lisa Orloff Clark, Astrid an Huef, and Iain Raeburn
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Published: 
June 27, 2013 
Keywords: 
Fell algebra; continuoustrace algebra; DixmierDouady invariant; the C*algebra of a local homeomorphism; groupoid C*algebra 
Subject: 
46L55 


Abstract
We study the groupoid C*algebra 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
continuoustrace 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
étale groupoids. The C*algebras of these relations are, up to Morita
equivalence, precisely the Fell algebras with trivial DixmierDouady
invariant as recently defined by an Huef, Kumjian and Sims. We use twisted groupoid
algebras to provide examples of Fell algebras with nontrivial DixmierDouady
invariant.


Author information
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand.
lclark@maths.otago.ac.nz
astrid@maths.otago.ac.nz
iraeburn@maths.otago.ac.nz

