On the uniqueness of the moonshine vertex operator algebra

TL;DR

This paper proves that under certain conditions, a vertex operator algebra is uniquely isomorphic to the moonshine VOA, advancing the understanding of its uniqueness and confirming a weak version of the FLM conjecture.

Contribution

It establishes the first results towards the weak version of the FLM uniqueness conjecture for the moonshine VOA.

Findings

Proved that certain conditions imply isomorphism to the moonshine VOA.

Established a weak form of the FLM uniqueness conjecture.

First results confirming the uniqueness of the moonshine VOA under specified conditions.

Abstract

It is proved that a vertex operator algebra is isomorphic to the moonshine VOA of Frenkel-Lepowsky-Meurman if it satisfies certain conditions. Our two main theorems establish a weak version of the FLM uniqueness conjecture for the moonshine vertex operator algebra. We believe that these are the first such results.