KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

• KAJIWARA Tsuyoshi

  Department of Environmental and Mathematical Sciences Okayama University

• WATATANI Yasuo

  Department of Mathematical Sciences Kyushu University

書誌事項

タイトル別名

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

抄録

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.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 67 (1), 83-104, 2013

  九州大学大学院数理学研究院

キーワード

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

詳細情報

• CRID: 1390001205227997696
• NII論文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
• 本文言語コード: en
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