2017/01/25 by Zahra Afsar, Afsar, Zahra, Astrid an Huef +3
Mathematics · Physics and Astronomy · #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1701.07183
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a family of *-commuting local homeomorphisms on a compact\nspace, and build a compactly aligned product system of Hilbert bimodules (in\nthe sense of Fowler). This product system has a Nica-Toeplitz algebra and a\nCuntz-Pimsner algebra. Both algebras carry a gauge action of a\nhigher-dimensional torus, and there are many possible dynamics obtained by\ncomposing with different embeddings of the real line in this torus. We study\nthe KMS states of these dynamics. For large inverse temperatures, we describe\nthe simplex of KMS states on the Nica-Toeplitz algebra. To study KMS states for\nsmaller inverse temperature, we consider a preferred dynamics for which there\nis a single critical inverse temperature. We find a KMS state on the\nNica-Toeplitz algebra at this critical inverse temperature which factors\nthrough the Cuntz-Pimsner algebra. We then illustrate our results by\nconsidering backward shifts on the infinite-path spaces of a class of\nk-graphs.\n