Extensions of pure C*-algebras

2025/06/12 by Francesc Perera, Perera, Francesc, Hannes Thiel +3
Mathematics · #Advanced Operator Algebra Research #Advanced Banach Space Theory #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2506.10529

Abstract

Given a closed ideal I in a C*-algebra A, we show that A is pure if and only if I and A/I are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure.

Citations

• Strict comparison in reduced group C^*-algebras
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• On the classification problem for nuclear C*-algebras
• Strongly self-absorbing C*-algebras

Related

• Pure C*-algebras
• Centrally pure C*-algebras
• Real rank of extensions of C*-algebras
• Semi-invertible extensions of C*-algebras
• Ideal structure and simplicity of the C*-algebras generated by Hilbert bimodules