Regularity properties in the classification program for separable amenable C*-algebras

Elliott, George; Toms, Andrew

doi:10.1090/S0273-0979-08-01199-3

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ISSN 1088-9485(online) ISSN 0273-0979(print)

Regularity properties in the classification program for separable amenable C-algebras

Authors: George A. Elliott and Andrew S. Toms
Journal: Bull. Amer. Math. Soc. 45 (2008), 229-245
MSC (2000): Primary 46L35; Secondary 46L80
Posted: February 12, 2008
MathSciNet review: 2383304
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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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