2013 Fiscal Year Final Research Report
Construction and classification of holomorphic vertex operator algebras of central charge 24
| Project/Area Number |
23540013
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tohoku University (2012-2013)
Aichi University of Education (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| 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 |
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| 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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