2020 Fiscal Year Final Research Report
Research on uniqueness of holomorphic vertex operator algebras of central charge 24 by using reverse orbifold construction
Project/Area Number |
17K05154
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Tohoku University |
Principal Investigator |
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Project Period (FY) |
2017-04-01 – 2021-03-31
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Keywords | 代数学 / 頂点作用素代数 / 正則頂点作用素代数 / 軌道体構成法 / リー代数 / リーチ格子 / 逆軌道体構成法 |
Outline of Final Research Achievements |
The classification of holomorphic vertex operator algebras of central charge 24 is one of famous problems in vertex operator algebra theory. The 71 candidates have been constructed, and the remaining problem is to prove that the vertex operator algebra structure is uniquely determined by the Lie algebra structure of the weight one subspace.
At the beginning of this research project, there are the remaining 41 holomorphic vertex operator algebras of central charge 24 whose uniqueness have not been proved yet. The main result is to prove the uniqueness of the 11 cases by using the reverse orbifold construction. Combining the results by us and other researchers, we have proved the uniqueness of holomorphic vertex operator algebras of central charge 24 with non-trivial weight one subspaces.
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Free Research Field |
頂点作用素代数
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Academic Significance and Societal Importance of the Research Achievements |
中心電荷24の正則頂点作用素代数には様々な階数24の正定値のユニモジュラ偶格子との類似が観察されている。本研究の研究成果はその根拠の一つとなるものである。また、階数24の正定値のユニモジュラ偶格子の応用範囲は頂点作用素代数のみならず、代数幾何学、整数論、組合せ論、有限群論など多岐にわたっている。同様に、中心電荷24の正則頂点作用素代数の他分野への応用も期待されており、その際には今回の成果が役立つ。
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