Decomposition rank and Z-stability

• 成果类型: Article
• 署名作者: Winter, Wilhelm
• 署名单位: University of Nottingham
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0216-4
• 发表日期: 2010
• 页码: 229-301
• 关键词: C-ASTERISK-ALGEBRAS; covering dimension; stable rank; real rank; K-THEORY; CLASSIFICATION; nuclear; Isomorphism

摘要

We show that separable, simple, nonelementary, 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.