Nuclear dimension and n-comparison

Abstract

It is shown that if a C*-algebra has nuclear dimension $n$ then its Cuntz semigroup has the property of $n$-comparison. It then follows from results by Ortega, Perera, and Rordam that $\sigma$-unital C*-algebras of finite nuclear dimension (and even of nuclear dimension at most $\omega$) are stable if and only if they have no non-zero unital quotients and no non-zero bounded traces.

changed introduction, added lemma

References in corpus (1)

• Completely positive maps of order zero

Cited by in corpus (10)

• Nuclear dimension of simple C*-algebras
• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• The Dixmier property and tracial states for C*-algebras
• Regularity for stably projectionless, simple C*-algebras
• Decomposable approximations revisited
• Characterizing classifiable AH algebras
• Absorbing representations with respect to closed operator convex cones
• Decomposable approximations and approximately finite dimensional C*-algebras
• Nuclear dimension of extensions of ${\mathcal{O}}_{\infty }$-stable algebras
• Faithful tracial states on quotients of C*-algebras