Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras

Lam, Ching Hung; Shimakura, Hiroki

doi:10.1090/tran/7887

Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
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by Ching Hung Lam and Hiroki Shimakura PDF

Trans. Amer. Math. Soc. 372 (2019), 7001-7024 Request permission

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 $24$ is uniquely determined by its weight $1$ Lie algebra if the Lie algebra has the type $E_{6,3}G_{2,1}^3$, $A_{2,3}^6$, or $A_{5,3}D_{4,3}A_{1,1}^3$.

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