Limits of KMS states on Toeplitz algebras of finite graphs
Abstract
The structure of KMS states of Toeplitz algebras associated to finite graphs equipped with the gauge action is determined by an HuefLacaRaeburnSims. 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 nonminimal components and the relation between vertices and minimal components in the KMSstructure. For each component $C_0$ and each vertex $v \in C_0$, 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 $C_0$ in the graph of components.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.08431
 arXiv:
 arXiv:2108.08431
 Bibcode:
 2021arXiv210808431T
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 21 pages. Minor Revisions are added in pp.1112