Inventiones mathematicae

, 179:229

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


DOI: 10.1007/s00222-009-0216-4

Cite this article as:
Winter, W. Invent. math. (2010) 179: 229. doi:10.1007/s00222-009-0216-4


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.

Mathematics Subject Classification (2000)

46L85 46L35 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUnited Kingdom

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