Research on comlex dynamical systems and C*-algebras
| Project/Area Number |
25287019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
幸崎 秀樹 九州大学, 数理学研究院, 学術研究者 (20186612)
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| Co-Investigator(Renkei-kenkyūsha) |
Matsui Taku 九州大学, 数理学研究院, 教授 (50199733)
Ueda Yoshimichi 名古屋大学, 多元数理科学研究科, 教授 (00314724)
Masuda Toshihiko 九州大学, 数理学研究院, 准教授 (60314978)
Kajiwara Tsuyoshi 岡山大学, 環境学研究科, 教授 (50169447)
Matsumoto Kengo 上越教育大学, 学校教育研究科, 教授 (40241864)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥11,830,000 (Direct Cost: ¥9,100,000、Indirect Cost: ¥2,730,000)
Fiscal Year 2017: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
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| Keywords | 作用素環 / 複素力学系 / 自己相似写像 / K-理論 / 次元群 / テント写像 / C*－環 / 極大可換環 / C*-環 / 自己相似 / トレース / Ｋ群 |
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| Outline of Final Research Achievements |
In this research, we associate C*-algebras with complex dynamical systems of iterations of rational functions R using Hilbert bimodule, and we have found interesting relations between operator algebras and complex dynamical systems. We can recover some properties of complex dynamical systems of R from the associated C*-algebras with the gauge action. We explain the structure of the singularity of branched points in terms of K-theory and KMS states for gauge actions. We determine the extreme points of the traces on the cores of the C*-algebras associated with self-similar maps. We find their ideal structure. We showed that the dimension group of the tent map is the free abelian infinite group and the shift on it.
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Report
(6 results)
Research Products
(18 results)
