2019 Fiscal Year Final Research Report
Group actions and von Neumann algebras
| Project/Area Number |
17K14201
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
Isono Yusuke 京都大学, 数理解析研究所, 特定助教 (80783076)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | フォンノイマン環 / 冨田・竹崎理論 / 離散群の非特異作用 / エルゴード理論 / アフィン変換 |
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| Outline of Final Research Achievements |
I am interested in von Neumann algebras arising from group actions on measure spaces. In the case that the action does not preserve any measure, the algebra becomes type III, which is the most difficult class in von Neumann algebras. I obtained the following two results.
First, I succeeded to generalize Popa's techniques to type III algebras. This is a technical result but is the most important part of my research.
Second, I established a new way of constructing group actions. This uses affine actions of groups, hence the structure of the action is closely related to geometry of the group.
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| Free Research Field |
作用素環論
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| Academic Significance and Societal Importance of the Research Achievements |
離散群の測度空間への作用は，測度を保つ作用が広く研究されている．これは測度を保たない群作用の研究が極めて難解である事が理由であり，よって多くの事が分かっていない．しかし一方で，幾何学的，または確率論的な着眼点から自然にそのような作用が現れる事もあるため，その研究には重要な意義がある．私の研究は，そのような作用に対する技術的な進展と具体例の構成であり，これはこの方面における基礎的な研究の一つとみなせるだろう．
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