Regularity properties in the classification program for separable amenable C$^*$-algebras
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- by George A. Elliott and Andrew S. Toms PDF
- Bull. Amer. Math. Soc. 45 (2008), 229-245 Request permission
Abstract:
We report on recent progress in the program to classify separable amenable C$^*$-algebras. Our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank, strict comparison of positive elements, and $\mathcal {Z}$-stability, and on the importance of the Cuntz semigroup. We include a brief history of the program’s successes since 1989, a more detailed look at the Villadsen-type algebras which have so dramatically changed the landscape, and a collection of announcements on the structure and properties of the Cuntz semigroup.References
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Additional Information
- George A. Elliott
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 2E4
- MR Author ID: 62980
- Email: elliott@math.toronto.edu
- Andrew S. Toms
- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3
- Email: atoms@mathstat.yorku.ca
- Received by editor(s): April 20, 2007
- Received by editor(s) in revised form: October 1, 2007
- Published electronically: February 12, 2008
- Additional Notes: This work was partially supported by the Natural Sciences and Engineering Research Council of Canada
- © Copyright 2008 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 45 (2008), 229-245
- MSC (2000): Primary 46L35; Secondary 46L80
- DOI: https://doi.org/10.1090/S0273-0979-08-01199-3
- MathSciNet review: 2383304