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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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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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 / 共形場理論 / 有限群 |
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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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Report
(5 results)
Research Products
(26 results)
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[Presentation] On Conway-Miyamoto correspondences2016
Author(s)
Hiroshi Yamauchi
Organizer
Workshop on Finite Groups, VOA, and Algebraic Combinatorics
Place of Presentation
Foguang University, Yilan county, Taiwan
Year and Date
2016-03-23
Related Report
Int'l Joint Research
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