A Self-Dual Integral Form of the Moonshine Module

Abstract

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and Ryba. As a corollary, we find that Griess's original 196884-dimensional representation of the monster admits a positive-definite self-dual integral form with monster symmetry.

References in corpus (8)

• Modular invariance of trace functions in orbifold theory
• Construction and Classification of Holomorphic Vertex Operator Algebras
• Notes on Grothendieck topologies, fibered categories and descent theory
• Generalized Moonshine IV: Monstrous Lie algebras
• On integral forms for vertex algebras associated with affine Lie algebras and lattices
• 51 constructions of the Moonshine module
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• ${\mathbb{Z}}_3$-orbifold construction of the Moonshine vertex operator algebra and some maximal $3$-local subgroups of the Monster

Cited by in corpus (3)

• On the tensor structure of modules for compact orbifold vertex operator algebras
• A Composite Order Generalization of Modular Moonshine
• Integral forms in vertex operator algebras, a survey