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The Dixmier-Douady class of groupoid crossed products

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Paul S. Muhly  and
Dana P. Williams
Paul S. Muhly
Affiliation:
Department of Mathematics, University of Iowa, Iowa City,, IA 52242, USA e-mail: pmuhly@math.uiowa.edu
Dana P. Williams
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, USA e-mail: dana.williams@dartmouth.edu
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Abstract

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We give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 223 - 234
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Echterhoff, S. and Williams, D. P., ‘Locally inner actions on C0(X)-algebras’, J. Operator Theory 45 (2001), 131–160.Google Scholar
[2]Fell, J. M. G. and Doran, R., Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles, Vol. I & II (Academic Press, New York, 1988).Google Scholar
[3]Fulman, I., Muhly, P. S. and Williams, D. P., ‘Continuous-trace groupoid crossed products’, Proc. Amer. Math. Soc. 132 (2004), 707–717.CrossRefGoogle Scholar
[4]Kumjian, A., Muhly, P. S., Renault, J. N. and Williams, D. P., ‘The Brauer group of a locally compact groupoid’, Amer. J. Math. 120 (1998), 901–954.CrossRefGoogle Scholar
[5]Muhly, P. S., Renault, J. and Williams, D. P., ‘Equivalence and isomorphism for groupoid C*-algebras’, J. Operator Theory 17 (1987), 3–22.Google Scholar
[6]Raeburn, I. and Rosenberg, J., ‘Crossed products of continuous-trace C*-algebras by smooth actions’, Trans. Amer. Math. Soc. 305 (1988), 1–45.Google Scholar
[7]Raeburn, I. and Williams, D. P., ‘Pull-backs of C*-algebras and crossed products by certain diagonal actions’, Trans. Amer. Math. Soc. 287 (1985), 755–777.Google Scholar
[8]Raeburn, I. and Williams, D. P., Morita equivalence and continuous-trace C*-algebras, Mathematical Surveys and Monographs 60 (American Mathematical Society, Providence, RI, 1998).CrossRefGoogle Scholar