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

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

2007-04-13

arxiv.org/abs/0704.1803v3

Mathematics

Operator Algebras

19 pages, to appear in Bull. AMS, April 2008

Scientific paper

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 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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