When universal edge-colored directed graph C^*-algebras are exact

2013/07/22 by Benton L. Duncan, Duncan, Benton
Mathematics · Physics and Astronomy · #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1307.5801

openalex publication_date 2013/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider when the universal C^*-algebras associated to edge-colored directed graphs are exact. Specifically, for countable edge-colored directed graphs we show that the universal C^*-algebra is exact if and only if the C^*-algebra is isomorphic to a graph C^*-algebra which occurs precisely when the universal and reduced C^*-algebras of the edge-colored directed graph are isomorphic.

Citations

• Pullback and Pushout Constructions in C*-Algebra Theory

Related

• Naimark’s problem for graph C^*-algebras
• A dichotomy for simple self-similar graph C^∗-algebras
• C*-algebras of labelled graphs II - Simplicity results
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras IV, pure infiniteness
• C^*-algebras of self-similar graphs over arbitrary graphs