# Journal of Operator Theory

Volume 90, Issue 2, Autumn 2023 pp. 545-568.

Limits of KMS states on Toeplitz algebras of finite graphs

**Authors**:
Takuya Takeishi

**Author institution:** Faculty of Arts and Sciences,
Kyoto Institute of Technology,
Matsugasaki, Sakyo-ku, Kyoto, 606-8585,
Japan

**Summary: ** In the structure of KMS states of Toeplitz algebras associated to finite graphs,
we clarify the role of non-minimal components, i.e., strongly connected components which do not correspond to type III KMS states.
For each component $C_0$ and each vertex $v \in C_0$, the KMS state 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 give a combinatorial characterisation of the condition that the coefficient of the KMS state associated to each minimal component is nonzero.

**DOI: **http://dx.doi.org/10.7900/jot.2022jan10.2388

**Keywords: **Toeplitz algebra, graph $C^*$-algebra, KMS state, $C^*$-dynamical system

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