Nuclear dimension and \mathcal Z Z -stability

2014/03/31 by Yasuhiko Sato, Stuart White, Wilhelm Winter · 75 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Combinatorics #Conjecture #Dimension (graph theory) #Holomorphic and Operator Theory #Mathematical analysis #Mathematics #Pure mathematics #Separable space #Simple (philosophy) #Stability (learning theory) #TRACE (psycholinguistics) #Unital #math.OA #msc:46L05 #msc:46L35

paper · pdf · doi:10.1007/s00222-015-0580-1

published in Inventiones mathematicae 202(2), 893-921 (Springer Science+Business Media) · 23 Pages. New section added. Invent. Math., to appear

arxiv created 2015/01/28 · openalex publication_date 2015/02/26 · arxiv updated 2015/11/30 · openalex created_date 2020/08/13 · openalex updated_date 2026/08/05

Abstract

Simple, separable, unital, monotracial and nuclear \mathrm C^* -algebras are shown to have finite nuclear dimension whenever they absorb the Jiang–Su algebra \mathcal Z tensorially. This completes the proof of the Toms–Winter conjecture in the unique trace case.

Citations

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• K-Theory for Operator Algebras
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• Strict comparison and Z-absorption of nuclear C*-algebras
• On the classification problem for nuclear C*-algebras