Research on von Neumann algebras from a viewpoint of their close relation with ergodic theory
| Project/Area Number |
19540206
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
YAMANOUCHI Takehiko Hokkaido University, 大学院・理学研究院, 准教授 (30241293)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2007 – 2009
|
| Project Status |
Completed (Fiscal Year 2009)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| 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 / 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 |
|---|
| 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.
|
Report
(4 results)
Research Products
(8 results)
