Construction and classification of holomorphic vertex operator algebras of central charge 24
Project/Area Number |
23540013
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Tohoku University (2012-2013) Aichi University of Education (2011) |
Principal Investigator |
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
Keywords | 代数学 / 頂点作用素代数 / 格子 / 自己同型群 / 軌道体構成法 / 正則頂点作用素代数 / アファインリー代数 / 枠付頂点作用素代数 / アフィンリー代数 / モンスター / グラフ / 枠付き頂点作用素代数 / 二次形式 / イジング元 |
Research Abstract |
The construction and classification of holomorphic vertex operator algebras of central charge 24 is a famous open problem. In 1993 existence of 71 holomorphic vertex operator algebras of central charge 24 is predicted, and in 1996, 39 of them are explicitly constructed. In this research, we construct nine new ones by using framed vertex operator algebra theory and orbifold construction. Since eleven new ones are obtained by other researchers, we know that there exist 59 holomorphic vertex operator algebras of central charge 24. This makes progress in the construction problem. In addition, we prove that there exist exactly 56 holomorphic framed vertex operator algebras of central charge 24. This makes progress in the classification problem.
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Report
(4 results)
Research Products
(42 results)