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arXiv · 1906.02066

The nuclear dimension of $\mathcal O_\infty$-stable $C^*$-algebras

Joan Bosa·James Gabe·Aidan Sims·Stuart White
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Abstract

We show that every nuclear $\mathcal O_\infty$-stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, $\mathcal O_\infty$-stable C*-algebras have nuclear dimension 1. We also characterise when $\mathcal O_\infty$-stable C*-algebras have finite decomposition rank in terms of quasidiagonality and primitive-ideal structure, and determine when full $\mathcal O_2$-stable *-homomorphisms have nuclear dimension 0.

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Joan Bosa, James Gabe, Aidan Sims, Stuart White. 2019-06-05. The nuclear dimension of $\mathcal O_\infty$-stable $C^*$-algebras. https://arxiv.org/abs/1906.02066

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