On unital absorbing extensions of C^*-algebras of stable rank one and real rank zero

2023/03/10 by Qingnan An, An, Qingnan, Zhicaho Liu +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2303.05897

Abstract

Suppose that A,B are nuclear, separable \rm C^*-algebras of stable rank one and real rank zero, A is unital simple, B is stable and (\rm K₀(B),\rm K₀⁺(B)) is weakly unperforated in the sense of Elliott \citeEll. We show that any unital extension with trivial index maps of A by B is absorbing.

Related

• Strict comparison and Z-absorption of nuclear C*-algebras
• KK-rigidity of simple nuclear C*-algebras
• Strongly self-absorbing property for inclusions of C^*-algebras with a finite Watatani index
• The Jiang-Su absorption for inclusions of unital C*-algebras
• On the independence of K-theory and stable rank for simple C*-algebras