Strict comparison and Z-absorption of nuclear C*-algebras

• 成果类型: Article
• 署名作者: Matui, Hiroki; Sato, Yasuhiko
• 署名单位: Chiba University; Kyoto University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-012-0084-4
• 发表日期: 2012
• 页码: 179-196
• 关键词: rohlin property; real rank; AUTOMORPHISMS; dimension; ELEMENTS

摘要

For any unital separable simple infinite-dimensional nuclear C (au)-algebra with finitely many extremal traces, we prove that -absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear C (au)-algebra with tracial rank zero is approximately divisible, and hence is -absorbing.