The structure of the Brauer group and crossed products of -linear group actions on

Authors:
Siegfried Echterhoff and Ryszard Nest

Journal:
Trans. Amer. Math. Soc. **353** (2001), 3685-3712

MSC (1991):
Primary 46L55; Secondary 22D25

DOI:
https://doi.org/10.1090/S0002-9947-01-02794-5

Published electronically:
May 4, 2001

MathSciNet review:
1837255

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Abstract | References | Similar Articles | Additional Information

For a second countable locally compact group and a second countable locally compact space let denote the equivariant Brauer group (for the trivial -space ) consisting of all Morita equivalence classes of spectrum fixing actions of on continuous-trace -algebras with spectrum . Extending recent results of several authors, we give a complete description of in terms of group cohomology of and Cech cohomology of . Moreover, if has a splitting group in the sense of Calvin Moore, we give a complete description of the -bundle structure of the crossed product in terms of the topological data associated to the given action and the bundle structure of the group -algebra of .

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Additional Information

**Siegfried Echterhoff**

Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany

Email:
echters@math.uni-muenster.de

**Ryszard Nest**

Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

Email:
rnest@math.ku.dk

DOI:
https://doi.org/10.1090/S0002-9947-01-02794-5

Received by editor(s):
March 9, 1999

Received by editor(s) in revised form:
March 3, 2000

Published electronically:
May 4, 2001

Article copyright:
© Copyright 2001
American Mathematical Society