On the nuclear dimension of strongly purely infinite C*-algebras

Abstract

We show that separable, nuclear and strongly purely infinite C*-algebras have finite nuclear dimension. In fact, the value is at most three. This exploits a deep structural result of Kirchberg and Rørdam on strongly purely infinite C*-algebras that are homotopic to zero in an ideal-system preserving way.

7 pages; v2 a few minor stylistic changes in the intro. This version is going to appear in Advances in Mathematics

References in corpus (4)

• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• The nuclear dimension of C*-algebras
• Decomposition rank and Z-stability
• On the classification of simple amenable $C\ast$-algebras with finite decomposition rank, II

Cited by in corpus (3)

• Equivariant Kirchberg-Phillips-type absorption for amenable group actions
• The nuclear dimension of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• Nuclear dimension of graph C${}^{\ast }$-algebras with Condition~(K)