The nuclear dimension of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras

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.

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

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Cited by in corpus (4)

• The Cuntz-Toeplitz algebras have nuclear dimension one
• Classification of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• Sturmian subshifts and their C*-algebras
• C*-algebras and their nuclear dimension