2010 Fiscal Year Final Research Report
Research for Hilbert C*-bimodules and their application to complex dynamical systems
| Project/Area Number |
19540218
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Okayama University |
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Principal Investigator |
KAJIWARA Tsuyoshi Okayama University, 大学院・環境学研究科, 教授 (50169447)
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| Co-Investigator(Renkei-kenkyūsha) |
WATATANI Yasuo 九州大学, 大学院・数理学研究院, 教授 (00175077)
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| Project Period (FY) |
2007 – 2010
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| Keywords | (自己評価書)C*環 / ヒルベルトC^*双加群 / 複素力学系 / 自己相似写像 / KMS state / K-群 |
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| Research Abstract |
We classified KMS states on C^*-algebras constructed from the dynamical system on Riemannian sphere by rational functions and self-similar maps. Especially, we have made a complete classification for rational function cases. We constructed C^*-algebras using Hilbert C^*-bimodules for algebraic correspondences, which are generalization of rational functions, and have got sufficient conditions for simplicity and pure infiniteness of such C^*-algebras. We constructed concrete examples of countable infinite basis for Hilbert C^*-modules constructed from dynamical systems which have branch points, for example, rational functions and self-similar maps.
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