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

Joan Bosa; James Gabe; Aidan Sims; Stuart White

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

Operator Algebras 2022-01-12 v2

Authors: Joan Bosa , James Gabe , Aidan Sims , Stuart White

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.

Keywords

nuclear dimension O_infinity-stable C*-algebras nuclear *-homomorphism decomposition rank quasidiagonality exact domain

Cite

@article{arxiv.1906.02066,
  title  = {The nuclear dimension of $\mathcal O_\infty$-stable $C^*$-algebras},
  author = {Joan Bosa and James Gabe and Aidan Sims and Stuart White},
  journal= {arXiv preprint arXiv:1906.02066},
  year   = {2022}
}

Comments

Small changes. This is the accepted version. Adv. Math., to appear

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

Abstract

Keywords

Cite

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