Strong classification of extensions of classifiable C*-algebras

Abstract

We show that certain extensions of classifiable C*-algebra are strongly classified by the associated six-term exact sequence in K-theory together with the positive cone of K_{0}-groups of the ideal and quotient. We apply our result to give a complete classification of graph C*-algebras with exactly one ideal.

29 pages

References in corpus (3)

• C*-Algebras over Topological Spaces: The Bootstrap Class
• E-Theory for C*-algebras over topological spaces
• Classifying $C^{\ast }$-algebras with both finite and infinite subquotients

Cited by in corpus (7)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Classification of real rank zero, purely infinite C*-algebras with at most four primitive ideals
• Strong classification of purely infinite Cuntz-Krieger algebras
• Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras
• Classification of graph C*-algebras with no more than four primitive ideals
• Geometric classification of unital graph C*-algebras of real rank zero