2010 Fiscal Year Final Research Report
Study on finiteness properties of vertex operator algebras
| Project/Area Number |
20740017
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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 | Ehime University |
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Principal Investigator |
ABE Toshiyuki Ehime University, 理工学研究科, 准教授 (30380215)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 頂点作用素代数 / 代数 / オービフォールド |
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| Research Abstract |
I have been working on a finiteness property called a C_2-cofiniteness property, for a vertex operator algebras. A fixed point subalgebra of a vertex operator algebra by its finite automorphism group is called an orbifold model. In the representation theory of vertex operator algebra there is a conjecture that if a vertex operator algebra has the C_2-cofiniteness property then so does any orbifold model of it. I have found necessary and sufficient conditions which make the conjecture true for commutative vertex algebras and Z_2-permutation orbifold models of vertex operator algebras. I also showed that Z_2-permutation orbifold models of the Virasoro vertex operator algebras having C_2-cofinittness property satisfy the C_2-cofiniteness condition.
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