English

Decomposition rank and Z-stability

Operator Algebras 2009-08-28 v2 Functional Analysis

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.

Keywords

Cite

@article{arxiv.0806.2948,
  title  = {Decomposition rank and Z-stability},
  author = {Wilhelm Winter},
  journal= {arXiv preprint arXiv:0806.2948},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T10:51:55.036Z