Continuous-trace groupoid $C^*$-algebras. III
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- by Paul S. Muhly, Jean N. Renault and Dana P. Williams
- Trans. Amer. Math. Soc. 348 (1996), 3621-3641
- DOI: https://doi.org/10.1090/S0002-9947-96-01610-8
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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 $C^{*}$-algebra $C^*(\mathcal {G},\lambda )$ 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 $\mathcal {G}$.References
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Bibliographic 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
- MR Author ID: 146950
- Email: renault@univ-orleans.fr
- Dana P. Williams
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
- MR Author ID: 200378
- Email: dana.williams@dartmouth.edu
- Received by editor(s): December 17, 1994
- Additional Notes: The first and third authors were partially supported by the National Science Foundation.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 3621-3641
- MSC (1991): Primary 46L05, 46L35
- DOI: https://doi.org/10.1090/S0002-9947-96-01610-8
- MathSciNet review: 1348867