On the classification problem for nuclear C*-algebras

2005/09/05 by Andrew S. Toms, Toms, Andrew S. · 7 citations
Mathematics · #46L35 #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0509103

openalex publication_date 2005/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a simple, unital AH algebra which is shape equivalent to its tensor product with any infinite-dimensional UHF algebra, has the same tracial simplex as the said tensor product, and yet is not isomorphic to it. An analogous result for automorphisms is also proved.

Cited by

• Subquadratic growth and uniform property \(Γ\)
• Schubert Calculus and uniform property Γ
• Centrally pure C*-algebras
• Tensorial Permanence of K-Stability for Diagonal AH-Algebras
• Selfless reduced free products and graph products of C^∗-algebras
• Inductive Limits of Subhomogeneous C^*-algebras with Hausdorff Spectrum
• Extensions of pure C*-algebras

Related

• Simple nuclear C*-algebras not equivariantly isomorphic to their opposites
• Classifying ^*-homomorphisms I: Unital simple nuclear C^*-algebras
• UHF slicing and classification of nuclear C*-algebras
• Applications of C^*-classification
• Structure of nuclear C*-algebras: From quasidiagonality to\n classification, and back again