On the Genus of the Moonshine Module

2017/08/20 by Gerald Höhn, Höhn, Gerald · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.1708.05990

28 pages, 17 tables

arxiv created 2017/08/20 · openalex publication_date 2017/08/20 · arxiv updated 2017/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Superconformal symmetry in a class of Schellekens theories
• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries

Related

• A nonmeromorphic extension of the moonshine module vertex operator algebra
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra
• Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
• Geometry of the Frenkel-Kac-Segal cocycle