| Project/Area Number |
17H06785
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto Institute of Technology (2018)
Kyoto University (2017) |
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Principal Investigator |
Takeishi Takuya 京都工芸繊維大学, 基盤科学系, 助教 (20784490)
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| Project Period (FY) |
2017-08-25 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 作用素環論 / C*-環論 / Bost--Connes系 / K-理論 / KMS状態 / 非可換幾何学 / C*-環の分類 / 解析学 / 代数学 |
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| Outline of Final Research Achievements |
The Bost--Connes C*-algebras are operator algebras coming from number fields. The classification problem of the Bost--Connes C*-algebras has been an important open problem. In this research, we have completely solved this problem. Concretely, we proved that for two number fields K and L, if two Bost--Connes C*-algebras A_K, A_L are isomporphic, then K and L are isomorphic. In addition, we worked on another type of C*-algebras coming from number fields. For this type of C*-algebras, we are writing an article on KMS-states.
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| Academic Significance and Societal Importance of the Research Achievements |
作用素環の同型・非同型を決定することは作用素環論の根源的な課題であり，今回得られた結果は作用素環論として非常に興味深い結果である．それにとどまらず，作用素環論と数論の２つの分野の分野横断的な研究（特に作用素環論の数論への応用）の可能性を感じさせる結果でもある．今回の結果を通じて得られた代数体の不変量に関する研究など，後に続く重要な研究課題が同時に生まれている．総合して，数学の様々な側面から見て価値を持つ研究結果が得られたと考えている．
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