The nuclear dimension of O∞-stable C⁎-algebras

摘要: We show that every nuclear O∞-stable⁎-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, O∞-stable C⁎-algebras have nuclear dimension 1. We also characterise when O∞-stable C⁎-algebras have finite decomposition rank in terms of quasidiagonality and primitive-ideal structure, and determine when full O 2-stable⁎-homomorphisms have nuclear dimension 0.