KMS states for generalized gauge actions on Cuntz-Krieger algebras (An application of the Ruelle-Perron-Frobenius Theorem)

2001/10/17 by Ruy Exel, Exel, Ruy
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.DS #math.MP #math.OA

paper · pdf · doi:10.48550/arxiv.math/0110183

Plain TeX, 8 pages

arxiv created 2001/10/17 · openalex publication_date 2001/10/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra O_A, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space Σ_A. The main result consists of an application of Ruelle's Perron-Frobenius Theorem to show that these automorphism groups admit a single KMS state.

Related

• KMS states on C^*-algebras associated to higher-rank graphs
• Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz--Krieger algebras
• KMS states of quasi-free dynamics on Pimsner algebras
• KMS states on quantum Cuntz-Krieger algebras
• KMS states on C*-algebras associated to expansive maps