A holomorphic vertex operator algebra of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$

TL;DR

This paper constructs a unique holomorphic vertex operator algebra with central charge 24, featuring a specific weight one Lie algebra of type A_{6,7}, expanding the classification of such algebras.

Contribution

It introduces a new construction of a holomorphic vertex operator algebra with a specified weight one Lie algebra of type A_{6,7}.

Findings

Constructed a holomorphic VOA of central charge 24.

Identified the weight one Lie algebra as type A_{6,7}.

Contributed to the classification of VOAs with central charge 24.

Abstract

In this article, we describe a construction of a holomorphic vertex operator algebras of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$.