Tracial approximate divisibility and stable rank one

2021/08/20 by Xuanlong Fu, Kang Li, Fu, Xuanlong +3
Mathematics · Physics and Astronomy · #46L05 #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2108.08970

openalex publication_date 2021/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every separable simple tracially approximately divisible C^*-algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we show that every (non-unital) finite simple \cal Z-stable C^*-algebra has stable rank one.

Related

• Strict comparison and stable rank one
• Tracial approximation and \cal Z-stability
• On Local AH algebras
• A classification of finite simple amenable \cal Z-stable C^*-algebras, I: C^*-algebras with generalized tracial rank one
• Hereditary uniform property Γ