K-theoretic rigidity and slow dimension growth

• 成果类型: Article
• 署名作者: Toms, Andrew
• 署名单位: Purdue University System; Purdue University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0273-8
• 发表日期: 2011
• 页码: 225-244
• 关键词: C-ASTERISK-ALGEBRAS; real rank; inductive limits; stable rank; cuntz semigroup; matrix algebras; CLASSIFICATION; reduction; STABILITY

摘要

Let A be an approximately subhomogeneous (ASH) C*-algebra with slow dimension growth. We prove that if A is unital and simple, then the Cuntz semigroup of A agrees with that of its tensor product with the Jiang-Su algebra (sic). In tandem with a result of W. Winter, this yields the equivalence of (sic)-stability and slow dimension growth for unital simple ASH algebras. This equivalence has several consequences, including the following classification theorem: unital ASH algebras which are simple, have slow dimension growth, and in which projections separate traces are determined up to isomorphism by their graded ordered K-theory, and none of the latter three conditions can be relaxed in general.