### Abstract

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.

Original language | English |
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Pages (from-to) | 83-104 |

Number of pages | 22 |

Journal | Kyushu Journal of Mathematics |

Volume | 67 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 25 2013 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Kyushu Journal of Mathematics*,

*67*(1), 83-104. https://doi.org/10.2206/kyushujm.67.83