Nuclear dimension and Z-stability

• 成果类型: Article
• 署名作者: Sato, Yasuhiko; White, Stuart; Winter, Wilhelm
• 署名单位: Kyoto University; University of Glasgow; University of Munster
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0580-1
• 发表日期: 2015
• 页码: 893-921
• 关键词: C-ASTERISK-ALGEBRAS; jiang-su algebra; star-algebras; inductive limits; decomposition rank; central-sequences; CLASSIFICATION; Finite

摘要

Simple, separable, unital, monotracial and nuclear C*-algebras are shown to have finite nuclear dimension whenever they absorb the Jiang-Su algebra Z tensorially. This completes the proof of the Toms-Winter conjecture in the unique trace case. The structure theory of simple nuclear C*-algebras is currently undergoing revolutionary progress, driven by the discovery of regularity properties of various flavours: topological, functional analytic and algebraic. Despite the diverse nature of these regularity properties, they are all satisfied by those classes of C*-algebras which have been successfully classified by K-theoretic data, and they all fail spectacularly for the exotic algebras in [30,40] which provide counterexamples to Elliott's classification conjecture. The observation that there are deep connections between these disparate properties was crystallised in the following conjecture of Toms and the third named author.