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

Ching Hung Lam, Hiroki Shimakura
2017 Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES  
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
more » ... ifold vertex operator algebra Vĝ Lg has group-like fusion. We also realize the construction proposed by Höhn for some special isometry of the Leech lattice of prime order.
doi:10.21915/bimas.2017102 fatcat:mn5b6vjgfbhodmdtzjx5rmpg5u