Study of group actions on operator algebras from K-theoretic aspect
| Project/Area Number |
18K03321
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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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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Chiba University |
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Principal Investigator |
Matui Hiroki 千葉大学, 大学院理学研究院, 教授 (40345012)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 作用素環 / 群作用 / 極小力学系 / 解析学 |
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| Outline of Final Research Achievements |
Classification of group actions is one of the most important subjects in the theory of operator algebras. In the collaboration with M. Izumi (Kyoto University), I completely classified outer actions on poly-Z groups on Kirchberg algebras. Such a broad classification result has not been known so far.
From minimal dynamical systems on the Cantor set, one can construct etale groupoids and groupoid C*-algebras. Recently, homology groups and topological full groups of these groupoids have attracted much attention. I proved that a long exact sequence of homology groups arises from a certain pair of etale groupoids.
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| Academic Significance and Societal Importance of the Research Achievements |
作用素環という無限次元の代数的な構造が持つ対称性の理解を深めることができた。解析学と代数学と幾何学が交錯する点が特徴的である。また、カントール集合という0次元の空間上の構造の対称性についても研究を行い、ホモロジー群を通して理解を深めた。作用素環とカントール集合は全く異なる対象ではあるが、直接目で見ることができない対称性を解明した点で価値観を共有している。
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Report
(6 results)
Research Products
(9 results)
