Vertex operator algebra

Summary

A vertex operator algebra is a graded vector space $V$ in which every vector $v$ gives a formal series $Y(v, z)$ of operators on $V$. These series satisfy a Jacobi identity, and $V$ carries an action of the Virasoro algebra. It is the algebraic form of the chiral part of a two-dimensional conformal field theory. Examples come from affine Lie algebras, from the Virasoro algebra itself and from even lattices. The moonshine module, a vertex operator algebra with the Monster group as automorphism group, was the key to the proof of monstrous moonshine.