KMS STATES ON FINITE-GRAPH <i>C</i><sup>∗</sup>-ALGEBRAS

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  • KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

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We study Kubo-Martin-Schwinger(KMS) states on finite-graph C∗-algebras with sinks and sources. We compare finite-graph C∗-algebras with C∗-algebras associated with complex dynamical systems of rational functions. We show that if the inverse temperature β is large, then the set of extreme β-KMS states is parametrized by the set of sinks of the graph. This means that the sinks of a graph correspond to the branched points of a rational function from the point of KMS states. Since we consider graphs with sinks and sources, left actions of the associated bimodules are not injective. Then the associated graph C∗-algebras are realized as (relative) Cuntz-Pimsner algebras studied by Katsura. We need to generalize Laca-Neshvyev's theorem of the construction of KMS states on Cuntz-Pimsner algebras to the case that left actions of bimodules are not injective.

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