Investigation of Hecke von Neumann algebras determined by equivalence relations and applications to automorphic forms
| Project/Area Number |
23740132
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Ritsumeikan University |
|---|
Principal Investigator |
AOI Hisashi 立命館大学, 理工学部, 准教授 (90396276)
|
|---|
| Project Period (FY) |
2011-04-28 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
|---|
| Keywords | 作用素環 / フォンノイマン環 / ヘッケ対 / ヘッケ作用素 / ヘッケ環 / 同値関係 / 保型形式 |
|---|
| Outline of Final Research Achievements |
We investigated Hecke von Neumann algebras which come from equivalence relations, and succeeded to determined their structures. By applying the notion of Schlichting complition, we proved that any such Hecke von Neumann algebras arise from Hecke pair of groups. It means that we can apply the theory of Hecke operator for groups to the Hecke von Neumann algebras. So our results is interesting in terms of the theory of automorphic forms.
We also succeeded to visualize some equivalence relations by using the mathematical software SageMath.
|
Report
(5 results)
Research Products
(6 results)
