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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Continuous-trace groupoid $C^{\displaystyle *}$-algebras. III


Authors: Paul S. Muhly, Jean N. Renault and Dana P. Williams
Journal: Trans. Amer. Math. Soc. 348 (1996), 3621-3641
MSC (1991): Primary 46L05, 46L35
MathSciNet review: 1348867
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Abstract: Suppose that ${\mathcal {G}}$ is a second countable locally compact groupoid with a Haar system and with abelian isotropy. We show that the groupoid $C^{\displaystyle *}$-algebra $C^{\displaystyle *} ({\mathcal {G}},\lambda )$ has continuous trace if and only if there is a Haar system for the isotropy groupoid ${\mathcal {A}}$ and the action of the quotient groupoid ${\mathcal {G}}/{\mathcal {A}}$ is proper on the unit space of ${\mathcal {G}}$.


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Additional Information

Paul S. Muhly
Affiliation: Department of Mathematics, University of Iowa \ Iowa City, Iowa 52242
Email: muhly@math.uiowa.edu

Jean N. Renault
Affiliation: Department of Mathematics, University of Iowa \ Iowa City, Iowa 52242; Département de Mathématiques, Université d’Orléans, 45067 Orléans Cedex 2, France
Address at time of publication: Départment de Mathématiques, Université d’Orléans, 45067 Orléans Cedex 2, France
Email: renault@univ-orleans.fr

Dana P. Williams
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
Email: dana.williams@dartmouth.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01610-8
PII: S 0002-9947(96)01610-8
Keywords: Locally compact groupoid, $C^{\displaystyle *}$-algebra, continuous trace
Received by editor(s): December 17, 1994
Additional Notes: The first and third authors were partially supported by the National Science Foundation.
Article copyright: © Copyright 1996 American Mathematical Society