Decomposition rank and Z-stability

Details Decomposition rank and Z-stability Decomposition rank and Z-stability

2008-06-18

arxiv.org/abs/0806.2948v2

Mathematics

Operator Algebras

Some small corrections and stylistic improvements; 72 pages; to appear in Invent. Math

Scientific paper

We show that separable, simple, unital C*-algebras with finite decomposition rank absorb the Jiang-Su algebra 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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