Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices
Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices
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DOI：
10.21915/bimas.2017102
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
C. Lam;Hiroki Shimakura
中科院分区：
文献类型：
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作者：
C. Lam;Hiroki Shimakura
In this article, we discuss a more uniform construction of all 71 holomorphic vertex operator algebras in Schellekens’ list using an idea proposed by G. Höhn. The main idea is to try to construct holomorphic vertex operator algebras of central charge 24 using some sublattices of the Leech lattice Λ and level p lattices. We study his approach and try to elucidate his ideas. As our main result, we prove that for an even unimodular lattice L and a prime order isometry g, the orbifold vertex operator algebra V ĝ Lg has group-like fusion. We also realize the construction proposed by Höhn for some special isometry of the Leech lattice of prime order.
