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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.

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  1. School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom

    Wilhelm Winter

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  1. Wilhelm Winter
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Correspondence to Wilhelm Winter.

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

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Winter, W. Decomposition rank and \(\mathcal{Z}\) -stability. Invent. math. 179, 229–301 (2010). https://doi.org/10.1007/s00222-009-0216-4

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  • DOI: https://doi.org/10.1007/s00222-009-0216-4

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