Rationality of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of arbitrary rank
Rationality of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of arbitrary rank
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当$L$是任意秩的非简并偶格时顶点代数$V_L^$的有理性
DOI：
10.1016/j.jalgebra.2008.10.009
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Yamskulna
中科院分区：
文献类型：
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作者：
G. Yamskulna
本文证明了顶点代数VL+是有理数的，如果L是有限秩的负定偶格，或如果L是有限秩的非退化偶格，既不是正定的也不是负定的.特别地，对于这样的偶格L，我们证明了顶点代数VL+的朱代数是半单的。这推广了Abe [T.张文，正定偶格L的顶点算子代数VL+的合理性，数学，Z。249（2）（2005）455-484]，其建立了当L是有限秩的正定偶格时VL+的合理性。
In this paper we prove that the vertex algebra VL+is rational if L is a negative definite even lattice of finite rank, or if L is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices L, we show that the Zhu algebras of the vertex algebras VL+are semisimple. This extends the result of Abe from [T. Abe, Rationality of the vertex operator algebra VL+for a positive definite even lattice L, Math. Z. 249 (2) (2005) 455–484] which establishes the rationality of VL+when L is a positive definite even lattice of finite rank.
顶点算子代数和模不变性
DOI：
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发表时间：
2020
期刊：
the Proceedings of the Conference on Vertex Operator Algebras, Number Theory and Related Topics
影响因子：
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作者：
Masahiko Miyamoto
通讯作者：
Masahiko Miyamoto