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Irreducible induced representations of Fell bundle $ C^*$-algebras


Authors: Marius Ionescu and Dana P. Williams
Journal: Trans. Amer. Math. Soc. 367 (2015), 5059-5079
MSC (2010): Primary 46L05, 46L55
DOI: https://doi.org/10.1090/S0002-9947-2014-06316-2
Published electronically: December 19, 2014
MathSciNet review: 3335410
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Abstract | References | Similar Articles | Additional Information

Abstract: We give precise conditions under which irreducible representations associated to stability groups induce to irreducible representations for Fell bundle $ C^*$-algebras. This result generalizes an earlier result of Echterhoff and the second author. Because the Fell bundle construction subsumes most other examples of $ C^*$-algebras constructed from dynamical systems, our result percolates down to many different constructions including the many flavors of groupoid crossed products.


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Additional Information

Marius Ionescu
Affiliation: Department of Mathematics, Colgate University, Hamilton, New York 13346
Address at time of publication: Department of Mathematics, United States Naval Academy, Annapolis, Maryland 21402
Email: mionescu@colgate.edu, ionescu@usna.edu

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/S0002-9947-2014-06316-2
Keywords: Fell bundle, irreducible representation, ideal structure, Fell bundle $C^{*}$-algebra
Received by editor(s): May 13, 2013
Published electronically: December 19, 2014
Additional Notes: The first and second authors were supported by individual grants from the Simons Foundation.
The second author would like to thank Marius and his colleagues at Colgate for a very pleasant and productive visit
Article copyright: © Copyright 2014 American Mathematical Society

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