Inducing primitive ideals
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- by Siegfried Echterhoff and Dana P. Williams PDF
- Trans. Amer. Math. Soc. 360 (2008), 6113-6129 Request permission
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.References
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Additional Information
- Siegfried Echterhoff
- Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, W-48149 Münster, Germany
- MR Author ID: 266728
- ORCID: 0000-0001-9443-6451
- Email: echters@math.uni-muenster.de
- Dana P. Williams
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
- MR Author ID: 200378
- Email: dana.williams@dartmouth.edu
- 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)
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2425706