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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Principal groupoid $ C^*$-algebras with bounded trace


Authors: Lisa Orloff Clark and Astrid an Huef
Journal: Proc. Amer. Math. Soc. 136 (2008), 623-634
MSC (2000): Primary 46L05, 46L55
Published electronically: October 26, 2007
MathSciNet review: 2358504
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Abstract: Suppose $ G$ is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids and show $ G$ is integrable if and only if the groupoid $ C^*$-algebra $ C^*(G)$ has bounded trace.


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Additional Information

Lisa Orloff Clark
Affiliation: Department of Mathematical Sciences, Susquehanna University, Selinsgrove, Pennsylvania 17870
Email: clarklisa@susqu.edu

Astrid an Huef
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: astrid@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09035-1
PII: S 0002-9939(07)09035-1
Keywords: Locally compact groupoid, $C^*$-algebra, bounded trace
Received by editor(s): August 23, 2006
Received by editor(s) in revised form: December 6, 2006
Published electronically: October 26, 2007
Additional Notes: This research was supported by the Australian Research Council and an AWM-NSF Mentoring Travel Grant.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society