Bulletin of the American Mathematical Society

Regularity properties in the classification program for separable amenable C

-algebras

Author(s): George A. Elliott; Andrew S. Toms
Journal: Bull. Amer. Math. Soc. 45 (2008), 229-245.
MSC (2000): Primary 46L35; Secondary 46L80
Posted: February 12, 2008
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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.

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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 46L35, 46L80

George A. Elliott
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 2E4
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

DOI: 10.1090/S0273-0979-08-01199-3
PII: S 0273-0979(08)01199-3
Keywords: {C}$^*$-algebras, classification
Received by editor(s): April 20, 2007,
Received by editor(s) in revised form: October 1, 2007
Posted: February 12, 2008
Additional Notes: This work was partially supported by the Natural Sciences and Engineering Research Council of Canada
Copyright of article: Copyright 2008, American Mathematical Society

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