Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras
Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras
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DOI：
10.1016/j.aim.2014.07.021
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
T. Arakawa;C. Lam;H. Yamada
中科院分区：
文献类型：
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作者：
T. Arakawa;C. Lam;H. Yamada
研究了准费米子顶点算子代数的朱氏代数、C2-代数和C2-余有限性。我们首先详细研究了仿射Kac-Moody李代数S Lˆ2的仿射顶点算子代数的朱氏代数和C2-代数，证明了它们具有相同的维且朱的代数是半单的。并建立了不可约模的分类。最后，我们证明了有限维单李代数的仿费米点算子代数是C2-余有限的。
We study Zhu's algebra, C 2-algebra and C 2-cofiniteness of parafermion vertex operator algebras. We first give a detailed study of Zhu's algebra and C 2-algebra of parafermion vertex operator algebras associated with the affine Kac–Moody Lie algebra s l ˆ 2. We show that they have the same dimension and Zhu's algebra is semisimple. The classification of irreducible modules is also established. Finally, we prove that the parafermion vertex operator algebras for any finite dimensional simple Lie algebras are C 2-cofinite.