, Volume 179, Issue 2, pp 229-301
Date: 12 Sep 2009

Decomposition rank and \(\mathcal{Z}\) -stability

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Abstract

We show that separable, simple, nonelementary, unital C*-algebras with finite decomposition rank absorb the Jiang–Su algebra \(\mathcal{Z}\) tensorially. This has a number of consequences for Elliott’s program to classify nuclear C*-algebras by their K-theory data. In particular, it completes the classification of C*-algebras associated to uniquely ergodic, smooth, minimal dynamical systems by their ordered K-groups.

Partially supported by EPSRC First Grant EP/G014019/1.