Research on von Neumann algebras from a viewpoint of their close relation with ergodic theory

从冯·诺依曼代数与遍历理论的密切关系研究冯·诺依曼代数

• 批准号: 19540206
• 负责人: YAMANOUCHI Takehiko
• 金额: $ 2.58万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540206/
• 关键词: 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; Hecke pair; Commensuarble; 部分因子間; Hecke環; Commensurable; almost normal; 因子環; 同値関係; 通約可能性

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.

在这项研究中，我研究了一类在算子代数领域被广泛研究的von Neumann代数，强调了它与遍历理论的密切联系。结果，首次揭示了算子代数中余作用的研究与遍历理论中的1-余循环完全相同。此外，本研究的分析还使得人们能够从算子代数的角度来研究遍历理论中已经建立的各种概念。这为从一个完全不同的角度研究遍历理论开辟了一条有趣的道路。

项目成果

Hecke von Neumann algebra of ergodic discrete measured equivalence relations

遍历离散测量等价关系的赫克·冯·诺依曼代数

• 期刊: Publications of Research Institute for Mathematical Sciences, Kyoto University (掲載決定)
• 作者: H. AOI;T;YAMANOUCHI
• 通讯作者: YAMANOUCHI

Normality for an inclusion of ergodic discrete measured equivalence relations in the von Neumann algebraic framework

冯诺依曼代数框架中包含遍历离散测量等价关系的正态性

• 发表时间: 2007
• 期刊: Journal of the Mathematical Society of Japan Vol. 59
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa;立川 篤;松山 登喜夫;T. YAMANOUCHI
• 通讯作者: T. YAMANOUCHI

Normality for an inclusion of ergodic discrete measured equivalence Relations in the von Neumann algebra framework

冯诺依曼代数框架中包含遍历离散测量等价关系的正态性

• 发表时间: 2007
• 期刊: Journal of the Mathematical Society of Japan 59
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa;立川 篤;松山 登喜夫;T. YAMANOUCHI;T. YAMANOUCHI;Takehiko Yamanouchi
• 通讯作者: Takehiko Yamanouchi

One-cocycles on smooth flows of weights and extended modular coactions

权重平稳流动和扩展模块化协作的单循环

• 发表时间: 2007
• 期刊: Ergodic Theory and Dynamical Systems Vol. 27
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa;立川 篤;松山 登喜夫;T. YAMANOUCHI;T. YAMANOUCHI
• 通讯作者: T. YAMANOUCHI

A characterization of a coaction reduced to that of a closed subgroup

共作用的表征简化为封闭子群的表征

• 发表时间: 2007
• 期刊: Tokyo Journal of Mathematics 30
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa;立川 篤;松山 登喜夫;T. YAMANOUCHI;T. YAMANOUCHI;Takehiko Yamanouchi;Hisashi Aoi
• 通讯作者: Hisashi Aoi