| Project/Area Number |
26610002
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 頂点作用素代数 / 有限単純群 / 自己同型群 / 軌道予想 / C2有限性 / 有理性 / 軌道理論 / 指標 / モジュラー不変性 / C2余有限性 / モンスター単純群 / 単純群 / 5次交代群 / 代数学 / 軌道構成 / ホロモルフィック頂点作用素代数 |
|---|
| Outline of Final Research Achievements |
For a few examples, it has shown that the orbifold theory of a good conformal field theory (CFT) by a finite automorphism is again good. The orbifold conjecture says that this is true for general cases, but there were no proofs. Recently, we have proved this conjecture for a finite solvable automorphism group. In order to complete this problem, we have to treat simple groups, which does not have linear representation.
In this research, we have introduced a new concept of tensor product of modules, on which we have very important Borcherds identity. As an application, we studied the orbifold theory for a few simple groups.
|
