2015 Fiscal Year Final Research Report
Research on vertex operator algebras and orthogonal groups of characteristic 3
| Project/Area Number |
24740027
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 頂点作用素代数 / ヴィラソロ代数 / ３互換群 / 直交群 / 散在型有限単純群 / フィッシャー群 |
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| Outline of Final Research Achievements |
I have studied 3-transposition groups, especially orthogonal groups of characteristic 3, acting on vertex operator algebras. The following are accomplished. (1) By considering Miyamoto involutions associated to Virasoro vectors of central charge 4/5 of sigma-type, I gave a construction of 3-transposition groups acting on vertex operator algebras, and also I provided a construction of vertex operator algebras based on linear codes over the field of order 4 on which 3-transposition groups act. In particular, I realized the orthogonal group of degree 8 over the field of order 3 as an automorphism group of a vertex operator algebra constructed from Hexacode. (2) I obtained a result determining the type of Miyamoto involutions based on 3-dimensional Griess algebras. (3) I formulated the Conway-Miyamoto correspondence between involutions of groups and Virasoro vectors of vertex operator algebras and I have established the correspondences for the second and third largest Fischer groups.
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| Free Research Field |
頂点作用素代数
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