On the Genus of the Moonshine Module

Abstract

We provide a novel and simple description of Schellekens' seventy-one affine Kac-Moody structures of self-dual vertex operator algebras of central charge 24 by utilizing cyclic subgroups of the glue codes of the Niemeier lattices with roots. We also discuss a possible uniform construction procedure of the self-dual vertex operator algebras of central charge 24 starting from the Leech lattice. This also allows us to consider the uniqueness question for all non-trivial affine Kac-Moody structures. We finally discuss our description from a Lorentzian viewpoint.

arXiv comment28 pages, 17 tables

References in corpus (4)

• Building vertex algebras from parts
• A holomorphic vertex operator algebra of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$
• Finite groups of symplectic automorphisms of hyperkähler manifolds of type $K{3}^{[2]}$
• ${\mathbb{Z}}_3$-orbifold construction of the Moonshine vertex operator algebra and some maximal $3$-local subgroups of the Monster

Cited by in corpus (8)

• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Schellekens' List and the Very Strange Formula
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions
• BPS Algebras in 2D String Theory
• Genus of vertex algebras and mass formula
• Lattices, Vertex Algebras and Modular Categories
• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries