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

• KAJIWARA Tsuyoshi

  Department of Environmental and Mathematical Sciences Okayama University

• WATATANI Yasuo

  Department of Mathematical Sciences Kyushu University

Bibliographic Information

Other Title

• KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

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.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 67 (1), 83-104, 2013

  Faculty of Mathematics, Kyushu University

Keywords

• <i>C</i>^∗-correspondences
• graph <i>C</i>^∗-algebras
• KMS states

Details

• CRID: 1390001205227997696
• NII Article ID: 130003364801
• DOI: 10.2206/kyushujm.67.83
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/67/1/67_083/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed