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Transactions of the American Mathematical Society

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Inducing primitive ideals


Authors: Siegfried Echterhoff and Dana P. Williams
Journal: Trans. Amer. Math. Soc. 360 (2008), 6113-6129
MSC (2000): Primary 46L55, 46L05
DOI: https://doi.org/10.1090/S0002-9947-08-04499-1
Published electronically: June 16, 2008
MathSciNet review: 2425706
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Abstract: We study conditions on a $ C^*$-dynamical system $ (A,G,\alpha)$ under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of $ G$ on the primitive ideal space $ \mathrm{Prim}(A)$ give primitive ideals (resp. irreducible representations) of the crossed product $ {A \rtimes_\alpha G}$. The results build on earlier results of Sauvageot and others and will correct a (possibly overly optimistic) statement of the first author. In an appendix, the first author takes the opportunity to fill a gap in the proof of an earlier result.


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Additional Information

Siegfried Echterhoff
Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, W-48149 Münster, Germany
Email: echters@math.uni-muenster.de

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/S0002-9947-08-04499-1
Received by editor(s): October 25, 2005
Received by editor(s) in revised form: February 12, 2007
Published electronically: June 16, 2008
Additional Notes: The authors were partly supported by the Ed Shapiro fund at Dartmouth College and the Deutsche Forschungsgemeinschaft (SFB 478)
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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