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

Joan Bosa; James Gabe; Aidan Sims; Stuart White

doi:10.1016/j.aim.2022.108250

The nuclear dimension of O_∞-stable C^⁎-algebras

Joan Bosa, James Gabe, Aidan Sims^*, Stuart White

^*Kontaktforfatter

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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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.

Originalsprog	Engelsk
Artikelnummer	108250
Tidsskrift	Advances in Mathematics
Vol/bind	401
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2022.108250
Status	Udgivet - 4. jun. 2022

Bibliografisk note

Funding Information:
Research partially supported by an Alexander von Humboldt Foundation Fellowship (SW), Australian Research Council grant DP180100595 (AS), a Carlsberg Foundation Internationalisation Fellowship (JG), by the DGI-MINECO and European Regional Development Fund through grant MTM2017-83487-P (JB), EPSRC:EP/R025061/1 (SW), and the Beatriu de Pinós postdoctoral programme of the Government of Catalonia's Secretariat for Universities and Research 2017-BP-0079 (JB).

Publisher Copyright:
© 2022 Elsevier Inc.

Dokumenter og links

10.1016/j.aim.2022.108250

Open access versionAccepteret manuskript, 510 KBLicens: CC BY-NC-ND

Citationsformater

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AU - Bosa, Joan

AU - Gabe, James

AU - Sims, Aidan

AU - White, Stuart

N1 - Funding Information: Research partially supported by an Alexander von Humboldt Foundation Fellowship (SW), Australian Research Council grant DP180100595 (AS), a Carlsberg Foundation Internationalisation Fellowship (JG), by the DGI-MINECO and European Regional Development Fund through grant MTM2017-83487-P (JB), EPSRC:EP/R025061/1 (SW), and the Beatriu de Pinós postdoctoral programme of the Government of Catalonia's Secretariat for Universities and Research 2017-BP-0079 (JB). Publisher Copyright: © 2022 Elsevier Inc.

PY - 2022/6/4

Y1 - 2022/6/4

N2 - 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.

AB - 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.

KW - C-algebra

KW - Nuclear dimension

U2 - 10.1016/j.aim.2022.108250

DO - 10.1016/j.aim.2022.108250

M3 - Journal article

AN - SCOPUS:85125894947

SN - 0001-8708

VL - 401

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108250

ER -