2001/12/05 by Alex Kumjian, Kumjian, Alex, David Pask +1
Mathematics · #46L05 #46L55 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0112049
Sixteen pages with no figures. To appear Ergodic Theory and Dynamical Systems
openalex publication_date 2001/12/05 · arxiv created 2002/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An action of \mathbb Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalises the construction of a topological Markov shift arising from a nonnegative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C^*(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.