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

Elliott, George; Toms, Andrew

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

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.

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