Uniqueness of vertex operator algebras arising from GKO-construction

TL;DR

This paper proves the uniqueness of certain vertex operator algebras constructed via GKO-construction, showing they are generated by their weight two subspace under specific conditions.

Contribution

It establishes the uniqueness of GKO-constructed vertex operator algebras and demonstrates they are generated by their weight two subspace, extending prior algebraic frameworks.

Findings

Vertex operator algebras from GKO-construction are unique under certain braiding matrix conditions.

These algebras are generated by their weight two subspace, the Griess algebra.

The work generalizes previous algebraic structures like 3A and 6A-algebras.

Abstract

A series of vertex operator algebras are constructed by GKO-construction, which is a generalization of 3A-algebra and 6A-algebra. It is proved their vertex operator algebra structures are unique under nonzero assumptions on some elements of braiding matrices. Furthermore, we show each of them is generated by weight two subspace, i.e. the Griess algebra.