Nuclear dimension of simple stably projectionless C*-algebras

Abstract

We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary C*-algebras.

arXiv comment40 pages. Fixed a typo in the statement of Theorem 2.7. Analysis & PDE, to appear

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Cited by in corpus (5)

• On classification of non-unital amenable simple C*-algebras, III, the range and the reduction
• The classification of Rokhlin flows on C*-algebras
• On tracial $\mathcal{Z}$-stability of simple non-unital C*-algebras
• Nuclear dimension of graph C${}^{\ast }$-algebras with Condition~(K)
• A characterization of the Razak-Jacelon algebra