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(Kenkyū-buntansha) |
綿谷 安男 九州大学, 大学院・数理学研究院, 教授 (00175077)
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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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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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 / 作用素環 / KMS状態 / ヒルベルトC*-双加群 / 代数コレスポンデンス / K群 / 代数correspondence / ヒルベルトC*双加群 |
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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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Report
(6 results)
Research Products
(36 results)
