KMS STATES ON FINITE-GRAPH <i>C</i><sup>∗</sup>-ALGEBRAS
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- KAJIWARA Tsuyoshi
- Department of Environmental and Mathematical Sciences Okayama University
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- WATATANI Yasuo
- Department of Mathematical Sciences Kyushu University
Bibliographic Information
- Other Title
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- KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS
Description
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
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- Kyushu Journal of Mathematics
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Kyushu Journal of Mathematics 67 (1), 83-104, 2013
Faculty of Mathematics, Kyushu University
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Details 詳細情報について
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- CRID
- 1390001205227997696
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- NII Article ID
- 130003364801
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- ISSN
- 18832032
- 13406116
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- HANDLE
- 2324/784528
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- KAKEN
- OpenAIRE
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- Abstract License Flag
- Disallowed