Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras

Abstract

In this article, we develop a general technique for proving the uniqueness of holomorphic vertex operator algebras based on the orbifold construction and its “reverse” process. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 24 is uniquely determined by its weight 1 1 Lie algebra if the Lie algebra has the type E 6 , 3 G 2 , 1 3 E_{6,3}G_{2,1}^3 , A 2 , 3 6 A_{2,3}^6 , or A 5 , 3 D 4 , 3 A 1 , 1 3 A_{5,3}D_{4,3}A_{1,1}^3 .