Simplicity of finitely-aligned k-graph C*-algebras

2008/10/25 by Jacob Shotwell, Shotwell, Jacob · 1 citation
Mathematics · #05C99 (Secondary) #46L05 (Primary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:05C99 #msc:46L05

paper · pdf · doi:10.48550/arxiv.0810.4567

12 pages

arxiv created 2008/10/25 · openalex publication_date 2008/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that no local periodicity is equivalent to the aperiodicity condition for arbitrary finitely-aligned k-graphs. This allows us to conclude that C*(Λ) is simple if and only if Λis cofinal and has no local periodicity.

Citations

• Removing sources from higher-rank graphs
• Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

Cited by

• Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra

Related

• On simple labelled graph C^*-algebras
• C*-algebras of labelled graphs II - Simplicity results
• Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs
• A dichotomy for simple self-similar graph C^∗-algebras
• The C^*-algebras of finitely aligned higher-rank graphs