Decomposition rank and Z-stability

Abstract

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.

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

References in corpus (3)

• Nonstable K-theory for Z-stable C*-algebras
• A universal property for the Jiang-Su algebra
• The Jiang-Su algebra revisited

Cited by in corpus (8)

• Nuclear dimension and Z-stability
• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• Strongly self-absorbing C*-dynamical systems
• Decomposable approximations of nuclear C*-algebras
• The Dixmier property and tracial states for C*-algebras
• Rokhlin dimension: absorption of model actions
• On the nuclear dimension of strongly purely infinite C*-algebras
• Decomposable approximations and approximately finite dimensional C*-algebras