Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices | Zendy

Ching Hung Lam | Zendy; Hiroki Shimakura | Zendy

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Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

Author(s) -

Ching Hung Lam,

Hiroki Shimakura

Publication year - 2017

Publication title -

bulletin of the institute of mathematics academia sinica new series

Language(s) - English

Resource type - Journals

eISSN - 2304-7909

pISSN - 2304-7895

DOI - 10.21915/bimas.2017102

Subject(s) - vertex (graph theory) , lattice (music) , leech , central charge , holomorphic function , operator (biology) , operator algebra , mathematics , pure mathematics , physics , combinatorics , computer science , mathematical analysis , conformal map , chemistry , graph , biochemistry , repressor , world wide web , acoustics , transcription factor , gene

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.

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