The classification problem for amenable C*-algebras: the non-simple case
by
George Elliott
Department of Mathematics , University of Copenhagen

The problem of obtaining a K-theoretical classification of separable amenable C*-algebras is reviewed, with particular emphasis given to the non-simple case. Excluding the case of type I algebras (not very far advanced!) and the case of real rank zero algebras (quite far advanced!), one has in the non-simple case so far only the classification of O(2)-stable algebras (Mortensen, Elliott-Fulman, and Kirchberg). An exception to this is the case considered by K. Stevens: inductive limits of direct sums of matrix algebras over the interval with the so-called ideal property, that closed two-sided ideals are generated by projections. Recently, the speaker and Fulman have succeeded in removing the assumption of the ideal property.

Date received: June 15, 2000