Quasidiagonality of nuclear C**-algebras

• 成果类型: Article
• 署名作者: Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.1.4
• 发表日期: 2017
• 页码: 229-284
• 关键词: inductive limits; z-stability; real rank; UNITARY EQUIVALENCE; decomposition rank; star-algebras; CLASSIFICATION; dimension; SUBALGEBRAS; conjecture

摘要

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C*-algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension. Finally, we confirm the Rosenberg conjecture: discrete, amenable groups have quasidiagonal C*-algebras.