KMS states on finite-graph C*-algebras

Details KMS states on finite-graph C*-algebras KMS states on finite-graph C*-algebras

2010-07-24

arxiv.org/abs/1007.4248v1

Mathematics

Operator Algebras

23 pages, LaTeX2e

Scientific paper

We study 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 $\beta$ is large, then the set of extreme $\beta$-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 funcition 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-Neshevyev'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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