Vol. 13, No. 7, 2020

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Nuclear dimension of simple stably projectionless $\mathrm{C}^*$-algebras

Jorge Castillejos and Samuel Evington

Vol. 13 (2020), No. 7, 2205–2240

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

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$\mathrm{C}^*$-algebras, classification of $\mathrm{C}^*$-algebras
Mathematical Subject Classification 2010
Primary: 46L05, 46L35
Received: 4 March 2019
Revised: 9 June 2019
Accepted: 13 August 2019
Published: 10 November 2020
Jorge Castillejos
Department of Mathematics
KU Leuven
Samuel Evington
School of Mathematics and Statistics
University of Glasgow
United Kingdom
Institute of Mathematics
Polish Academy of Sciences