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Continuous-trace groupoid crossed products

Authors: Igor Fulman, Paul S. Muhly and Dana P. Williams
Journal: Proc. Amer. Math. Soc. 132 (2004), 707-717
MSC (2000): Primary 46L35, 46L55
Published electronically: October 15, 2003
MathSciNet review: 2019947
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Abstract: Let $G$ be a second countable, locally compact groupoid with Haar system, and let $\mathcal{A}$ be a bundle of $C^{\ast}$-algebras defined over the unit space of $G$ on which $G$ acts continuously. We determine conditions under which the associated crossed product $C^{\ast}(G;\mathcal{A})$is a continuous trace $C^{\ast}$-algebra.

References [Enhancements On Off] (What's this?)

  • 1. P. Bernat, N. Conze, M. Duflo, M. Lévy-Nahas, M. Raïs, P. Renouard, and M. Vergne, Représentations des groupes de Lie résolubles, Dunod, Paris, 1972, Monographies de la Société Mathématique de France, No. 4. MR 56:3183
  • 2. Klaus Deicke, Pointwise unitary coactions on $C^{*} $-algebras with continuous trace, J. Operator Theory 43 (2000), no. 2, 295-327. MR 2001d:46098
  • 3. Jacques Dixmier, $C^*$-algebras, North-Holland Mathematical Library, vol. 15, North-Holland, New York, 1977. MR 56:16388
  • 4. J. M. G. Fell and Robert Doran, Representations of $*$-algebras, locally compact groups, and Banach $*$-algebraic bundles, vols. I & II, Academic Press, New York, 1988. MR 90c:46001, MR 90c:46002
  • 5. Philip Green, $C^*$-algebras of transformation groups with smooth orbit space, Pacific J. Math. 72 (1977), 71-97. MR 56:12170
  • 6. -, The local structure of twisted covariance algebras, Acta Math. 140 (1978), 191-250. MR 58:12376
  • 7. Alexander Kumjian, Paul S. Muhly, Jean N. Renault, and Dana P. Williams, The Brauer group of a locally compact groupoid, Amer. J. Math. 120 (1998), 901-954. MR 2000b:46122
  • 8. Ru Ying Lee, On the $C^*$-algebras of operator fields, Indiana Univ. Math. J. 25 (1976), 303-314. MR 53:14150
  • 9. Paul S. Muhly, Jean Renault, and Dana P. Williams, Equivalence and isomorphism for groupoid $C^*$-algebras, J. Operator Theory 17 (1987), 3-22. MR 88h:46123
  • 10. Paul S. Muhly and Dana P. Williams, Continuous trace groupoid $C^*$-algebras, Math. Scand. 66 (1990), 231-241. MR 91j:46081
  • 11. -, Continuous trace groupoid $C^*$-algebras. II, Math. Scand. 70 (1992), 127-145. MR 93i:46117
  • 12. May Nilsen, $C^*$-bundles and $C_0(X)$-algebras, Indiana Univ. Math. J. 45 (1996), 463-477. MR 98e:46075
  • 13. Dorte Olesen and Iain Raeburn, Pointwise unitary automorphism groups, J. Funct. Anal. 93 (1990), 278-309. MR 92b:46105
  • 14. Iain Raeburn and Jonathan Rosenberg, Crossed products of continuous-trace $C^*$-algebras by smooth actions, Trans. Amer. Math. Soc. 305 (1988), 1-45. MR 89e:46077
  • 15. Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace $C^*$-algebras, Mathematical Surveys and Monographs, vol. 60, American Mathematical Society, Providence, RI, 1998. MR 2000c:46108
  • 16. Jean Renault, Représentations des produits croisés d'algèbres de groupoïdes, J. Operator Theory 18 (1987), 67-97. MR 89g:46108
  • 17. Masamichi Takesaki, A liminal crossed product of a uniformly hyperfinite ${C}\sp{\ast} $-algebra by a compact Abelian automorphism group, J. Functional Analysis 7 (1971), 140-146. MR 43:941
  • 18. Dana P. Williams, The topology on the primitive ideal space of transformation group $C^*$-algebras and CCR transformation group $C^*$-algebras, Trans. Amer. Math. Soc. 266 (1981), 335-359. MR 82h:46081

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Additional Information

Igor Fulman
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804

Paul S. Muhly
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Dana P. Williams
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551

Received by editor(s): June 14, 2002
Published electronically: October 15, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society

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