On the classification problem for nuclear C*-algebras

• 成果类型: Article
• 署名作者: Toms, Andrew S.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.1029
• 发表日期: 2008
• 页码: 1029-1044
• 关键词: inductive limits; stable rank; THEOREM; Finite

摘要

We exhibit a counterexample to Elliott's classification conjecture for simple, separable, and nuclear C*-algebras whose construction is elementary, and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves. The consequences for the program to classify nuclear C*-algebras are far-reaching: one has, among other things, that existing results on the classification of simple, unital AH algebras via the Elliott invariant of K-theoretic data are the best possible, and that these cannot be improved by the addition of continuous homotopy invariant functors to the Elliott invariant.