Tracial approximation in simple C*-algebras

作者：Fu, Xuanlong^*; Lin, Huaxin

来源：Canadian Journal of Mathematics, 2022, 74(4): 942-1004.

DOI：10.4153/S0008414X21000158

• ASYMPTOTIC UNITARY EQUIVALENCE
• TOPOLOGICAL RANK
• DIMENSION FUNCTIONS
• COVERING DIMENSION
• DECOMPOSITION RANK
• NUCLEAR DIMENSION
• STAR-ALGEBRAS
• REAL RANK
• CLASSIFICATION
• STABILITY

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable infinite dimensional C*-algebra A is asymptotically tracially in the class of C*-algebras with finite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear Z-stable C*-algebras.

• 单位
  复旦大学