2017 / March Volume 12 No.1
Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices
| Published Date |
2017 / March
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|---|---|
| Title | Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices |
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| Pagination | 39-70 |
| Abstract | 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. H\"ohn. The main idea is to try to construct holomorphic vertex operator algebras of central charge $24$ using some sublattices of the Leech lattice $\Lambda$ 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 $V_{L_g}^{\hat{g}}$ has group-like fusion. We also realize the construction proposed by H\"ohn for some special isometry of the Leech lattice of prime order.
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| DOI | |
| AMS Subject Classification |
17B69.
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| Received |
2016-11-30
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