The equivariant Brauer groups of commuting

free and proper actions are isomorphic

Authors:
Alexander Kumjian, Iain Raeburn and Dana P. Williams

Journal:
Proc. Amer. Math. Soc. **124** (1996), 809-817

MSC (1991):
Primary 46L05, 46L35

DOI:
https://doi.org/10.1090/S0002-9939-96-03146-2

MathSciNet review:
1301034

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a locally compact space which admits commuting free and proper actions of locally compact groups and , then the Brauer groups and are naturally isomorphic.

**1.**F. Combes,*Crossed products and Morita equivalence*, Proc. London Math. Soc. (3)**49**(1984), 289--306. MR**86c:46081****2.**David Crocker, Alex Kumjian, Iain Raeburn, and Dana P. Williams,*An equivariant Brauer group and actions of groups on -algebras*, preprint.**3.**Raul E. Curto, Paul Muhly, and Dana P. Williams,*Crossed products of strongly Morita equivalent -algebras*, Proc. Amer. Math. Soc.**90**(1984), 528--530. MR**85i:46083****4.**Jacques Dixmier,*-algebras*, North-Holland, New York, 1977.MR**56:16388****5.**Edward Effros,*Transformation groups and -algebras*, Ann. of Math. (2)**81**(1965), 38--55. MR**30:5175****6.**J. M. G. Fell,*An extension of Mackey's method to Banach -algebraic bundles*, Mem. Amer. Math. Soc.**90**(1969), 1--168. MR**41:4255****7.**Philip Green,*-algebras of transformation groups with smooth orbit space*, Pacific J. Math.**72**(1977), 71--97. MR**56:12170****8.**------*The local structure of twisted covariance algebras*, Acta Math.**140**(1978), 191--150. MR**58:12376****9.**Kjeld Knudsen Jensen and Klaus Thomsen,*Elements of -theory*, Birkhäuser, Boston, 1991.MR**94b:19008****10.**Iain Raeburn,*On the Picard group of a continuous-trace -algebra*, Trans. Amer. Math. Soc.**263**(1981), 183--205. MR**82b:46090****11.**------*Induced -algebras and a symmetric imprimitivity theorem*, Math. Ann.**280**(1988), 369--387. MR**90k:46144****12.**Iain Raeburn and Jonathan Rosenberg,*Crossed products of continuous-trace -algebras by smooth actions*, Trans. Amer. Math. Soc.**305**(1988), 1--45. MR**89e:46077****13.**Iain Raeburn and Dana P. Williams,*Pull-backs of -algebras and crossed products by certain diagonal actions*, Trans. Amer. Math. Soc.**287**(1985), 755--777. MR**86m:46054****14.**Marc A. Rieffel,*Unitary representations of group extensions: An algebraic approach to the theory of Mackey and Blattner*, Adv. in Math. Suppl. Stud.**4**(1979), 43--81. MR**81h:22004****15.**------*Applications of strong Morita equivalence to transformation group -algebras*, Proc. Sympos. Pure Math., vol. 38, Part I, Amer. Math. Soc., Providence, RI, 1982, pp. 299--310. MR**84k:46046**

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Additional Information

**Alexander Kumjian**

Affiliation:
Department of Mathematics, University of Nevada, Reno, Nevada 89557

Email:
alex@math.unr.edu

**Iain Raeburn**

Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia

Email:
iain@math.newcastle.edu.au

**Dana P. Williams**

Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551

Email:
dana.williams@dartmouth.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03146-2

Keywords:
Crossed product,
continuous-trace,
$C^*$-algebra,
Morita equivalence

Received by editor(s):
August 30, 1994

Additional Notes:
The third author was partially supported by the National Science Foundation.

This research was supported by the Australian Department of Industry, Science, and Tech- nology.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society