2014 Fiscal Year Final Research Report
Study on finiteness conditions of orbifold models of vertex operator algebras
| Project/Area Number |
23740022
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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 | Ehime University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 頂点作用素代数 / オービフォールド模型 / Virasoro 代数 / C_2-余有限性 |
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| Outline of Final Research Achievements |
In Representation theory of vertex operator algebras, the finiteness condition called C_2-cofiniteness is one of important condition. The condition make finitely generated modules finite length although the verification is very difficult except for special cases. For example, an orbifold of C_2-cofinite vertex operator algebra by an automorphism has been believed to be C_2-cofinite for long time (Recently, this fact was proved by Miyamoto). On this research, I proved that for an arbitrary 2-subgroup G of the symmetric group S_n, the G-permutation orbifold of a C_2-cofinite vertex operator algebra is also C_2-cofinite. I also found an explicit structure of certain commutant of a 4-cyclic permutation orbifold model of an affine vertex operator algebra of type A_1 and level 1.
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| Free Research Field |
頂点作用素代数の表現論
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