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
Abstract

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