KMS states on finite-graph C*-algebras

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)83-104
Number of pages22
JournalKyushu Journal of Mathematics
Volume67
Issue number1
DOIs
Publication statusPublished - Jul 25 2013

Fingerprint

Graph C*-algebra
Finite Graph
Cuntz Algebra
Bimodule
Injective
Rational function
Graph in graph theory
Complex Dynamical Systems
C*-algebra
Extremes
Generalise
Theorem

Keywords

  • C*-correspondences
  • Graph C*-algebras
  • KMS states

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

KMS states on finite-graph C*-algebras. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Kyushu Journal of Mathematics, Vol. 67, No. 1, 25.07.2013, p. 83-104.

Research output: Contribution to journalArticle

Kajiwara, Tsuyoshi ; Watatani, Yasuo. / KMS states on finite-graph C*-algebras. In: Kyushu Journal of Mathematics. 2013 ; Vol. 67, No. 1. pp. 83-104.
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