2011 Fiscal Year Final Research Report
Fischer groups based on vertex operator algebras
| Project/Area Number |
21740011
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo Woman's Christian University (2010-2011)
Aichi University of Education (2009) |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | フィッシャー群 / 頂点作用素代数 / 散在型有限単純群 / ヴィラソロ代数 |
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| Research Abstract |
We study the vertex operator algebra VF which affords a natural action of the largest Fischer group of degree 24.We discovered a correspondence between the transpositions of the Fischer group and c=6/7 Virasoro vertex operator subalgebras of VF. Based on this correspondence, we obtained a framework which enables us to explain the 3 transposition property of the Fischer group and a mysterious relation between the largest Fischer group and the extended E6 Dynkin diagram. We also study the vertex operator superalgebra VB which affords a natural action of the Baby-monster sporadic simple group and found a one-to-one correspondence between the transpositions of the Baby-monster and c=7/10 Virasoro vertex operator subalgebras of VB. The 4-transposition property of the Baby-monster and its relation to the extended E7 Dynkin diagram is also explained via our results. We derived trace formulae for the extended Griess algebras which generalize the Matsu-Norton trace formulae and we found its fruitful applications to the sporadic finite simple groups.
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Research Products
(16 results)
