2009 Fiscal Year Final Research Report
Research on von Neumann algebras from a viewpoint of their close relation with ergodic theory
| Project/Area Number |
19540206
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
YAMANOUCHI Takehiko Hokkaido University, 大学院・理学研究院, 准教授 (30241293)
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| Co-Investigator(Kenkyū-buntansha) |
KISHIMOTO Akitaka 北海道大学, 大学院・理学研究院, 教授 (00128597)
AOI Hisashi 立命館大学, 理工学部, 准教授 (90396276)
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| Project Period (FY) |
2007 – 2009
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| Keywords | フォンノイマン環 / エルゴード理論 / 測度付き同値関係 / 部分因子環 / コサイクル / 余作用 / ヘッケ環 / 数論 |
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| Research Abstract |
In this research, I studied a certain class of von Neumann algebras extensively treated in the area of operator algebras, with an emphasis on its close connection with ergodic theory. As a result, it has for the first time been revealed that the study of coactions in operator algebras is exactly the same as that of 1-cocycles in ergodic theory. Moreover, the analysis made in this research has enabled one to study a various kind of concepts already established in ergodic theory from a viewpoint of operator algebras. This opens an intriguing way of making a research on ergodic theory from a totally different angle.
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