2015 Fiscal Year Final Research Report
Research of complex dynamical systems and C*-algebras
| Project/Area Number |
23540242
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
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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) |
2011-04-28 – 2016-03-31
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| Keywords | C*-環 / 複素力学系 / 自己相似写像 / 双加群 / トレース / イデアル / KMS 状態 |
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| Outline of Final Research Achievements |
We showed that graph C*-algebras have finite type KMS stated associated with sinks of the graphs. We showed that we can recover the information of the backward orbits of branched points from KMS states of the C*-algebras associated with the dynamics of rational functions on the Riemannian sphere.
We classified finite traces on the cores of the C*-algebras associated with self-similar maps under a technical assumption for branched points. Moreover, we described the matrix representation of the finite cores of the C*-algebras associated with self-similar maps, and using the matrix representation, we classified ideals of the core of the C*-algebras associated with self-similar maps under the same assumption.
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| Free Research Field |
作用素環論
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