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The nuclear dimension of O-stable C-algebras

Journal Article


Abstract


  • 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 O2-stable ⁎-homomorphisms have nuclear dimension 0.

Publication Date


  • 2022

Citation


  • Bosa, J., Gabe, J., Sims, A., & White, S. (2022). The nuclear dimension of O-stable C-algebras. Advances in Mathematics, 401. doi:10.1016/j.aim.2022.108250

Scopus Eid


  • 2-s2.0-85125894947

Web Of Science Accession Number


Volume


  • 401

Abstract


  • 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 O2-stable ⁎-homomorphisms have nuclear dimension 0.

Publication Date


  • 2022

Citation


  • Bosa, J., Gabe, J., Sims, A., & White, S. (2022). The nuclear dimension of O-stable C-algebras. Advances in Mathematics, 401. doi:10.1016/j.aim.2022.108250

Scopus Eid


  • 2-s2.0-85125894947

Web Of Science Accession Number


Volume


  • 401