# Journal of Operator Theory

Volume 75, Issue 1, Winter 2016 pp. 119-138.

KMS states
for quasi-free actions on finite-graph algebras

**Authors**:
Christopher Chlebovec

**Author institution:** UNB, Fredericton, NB, E3B 5A3, Canada

**Summary: **Given a graph $E$ and a labeling map $\omega$, we consider the
quasi-free action $\alpha^{\omega}$ of $\mathbb{R}$ on the graph algebra $C^{\ast}(E)$.
For a finite graph $E$, we give a complete characterization of all $\text{KMS}_{\beta}$
states of a graph algebra in terms of a polyhedral set in $\mathbb{R}^{E^0}$.
This characterization allows us to generalize the results of an Huef, Laca,
Raeburn, and Sims. We make an explicit construction
of all $\text{KMS}_{\beta}$ states for $\beta$ above a critical inverse temperature
$\beta_\mathrm c,$ as well as a precise description of the KMS states for
graphs with a certain strongly connected subgraph. In addition, we find a
correspondence between the $\text{KMS}$ states of a graph algebra and its
dual-graph algebra when $E$ is a row-finite graph with no sinks.

**DOI: **http://dx.doi.org/10.7900/jot.2014nov10.2050

**Keywords: **KMS states, graph algebras, quasi-free actions, $
C^{\ast}$-dynamical systems

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