Pure infiniteness, stability and C*-algebras of graphs and dynamical systems

1999/06/29 by Jacob v. B. Hjelmborg, Jacob Hjelmborg, Hjelmborg, Jacob v. B.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/9906201

31 pages

arxiv created 1999/06/29 · openalex publication_date 1999/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Pure infiniteness (in sense of E.Kirchberg and M.Rørdam) is considered for C*-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A of an infinite matrix A, admit characterizations of pure infiniteness. As a consequence, these generalized Cuntz-Krieger algebras are traceless if and only if they are purely infinite. Also, a characterization of AF-algebras among these C*-algebras is given. In the case of graph-algebras of locally finite graphs, characterizations of stability are obtained.

Related

• Purely infinite labeled graph C^*-algebras
• Cuntz-Krieger algebras for infinite matrices
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras IV, pure infiniteness
• Cuntz-like algebras
• Stability of C*-algebras associated to graphs