Limits of KMS states on Toeplitz algebras of finite graphs

2021/08/19 by Takuya Takeishi, Takeishi, Takuya
Mathematics · #Advanced Operator Algebra Research #Random Matrices and Applications #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2108.08431

Abstract

The structure of KMS states of Toeplitz algebras associated to finite graphs equipped with the gauge action is determined by an Huef--Laca--Raeburn--Sims. Their results imply that extremal KMS states of type I correspond to vertices, while extremal KMS states at critical inverse temperatures correspond to minimal strongly connected components. The purpose of this article is to clarify the role of non-minimal components and the relation between vertices and minimal components in the KMS-structure. For each component C₀ and each vertex v ∈ C₀, the KMS states at the critical inverse temperature of v obtained by the limit of type I KMS states associated to v uniquely decomposes into a convex combination of KMS states associated to minimal components. We show that for each minimal component C, the coefficient of the KMS state associated to C is nonzero if and only if there exists a maximal path from C to C₀ in the graph of components.

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