Monstrous moonshine MOC

Vertex operator algebra

A vertex operator algebra is a Vertex algebra which carries a representation of the Virasoro algebra, voa specifically there is a distinguished homogenous conformal element with vertex operator such that[^1988]

where

1. ;
2. for homogenous ; and
3. .

Properties

\begin{align*} [L(-1), Y(v,z)] = Y(L(-1)v, z) \end{align*}

\begin{align*} n \geq -1 \implies L(n)\mathbb{1} = 0 \end{align*}

\begin{align*} L(0) \omega = 2\omega \end{align*}