Integral forms in vertex operator algebras which are invariant under finite groups

TL;DR

This paper constructs positive definite integral forms in vertex operator algebras that are invariant under finite automorphism groups, with applications to the Moonshine VOA and lattice type VOAs.

Contribution

It proves the existence of invariant integral forms in certain VOAs, including the Moonshine VOA, expanding understanding of their algebraic structure.

Findings

Existence of invariant integral forms in lattice type VOAs

Construction of an invariant integral form in the Moonshine VOA

Examples of invariant forms in other lattice VOAs

Abstract

For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA which is invariant under the Monster, and examples in other lattice type VOAs.