2013 Fiscal Year Final Research Report
Research on vertex operator algebras associated with parafermion algebras
| Project/Area Number |
23540009
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
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| Research Collaborator |
ARAKAWA Tomoyuki 京都大学, 数理解析研究所, 准教授 (40377974)
TANABE Kenichiro 北海道大学, 大学院・理学研究院, 准教授 (10334038)
CHING Hung Lam Academia Sinica(台湾), 教授
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| Project Period (FY) |
2011 – 2013
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| Keywords | 頂点作用素代数 / パラフェルミオン代数 / アフィンリー代数 / W代数 |
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| Research Abstract |
We study parafermion vertex operator algebras, which are subalgebras of integrable representations of affine Lie algebras of type A1. Using singular vectors, we classify the irreducible modules for the parafermion vertex operator algebras. Furthermore, C2-cofiniteness is established. It is proved that the dimension of Zhu's algebra coincides with that of C2 algebra. The orbifold of a lattice vertex operator algebra associated with a square root 2 times an ordinary root lattice of type An by an automorphism of order 3 is studied. We classify the irreducible modules for the orbifold. The rationality and C2-cofiniteness of the orbifold are also established.
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