KMS states on the C*-algebras of finite graphs

2012/05/10 by Astrid an Huef, Huef, Astrid an, Marcelo Laca +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.1205.2194

openalex publication_date 2012/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value β_c, we give an explicit construction of all the KMS_β states. If the graph is strongly connected, then there is a unique KMS_βc state, and this state factors through the quotient map onto the C*-algebra C*(E) of the graph. Our approach is direct and relatively elementary.

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