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

arXiv comment27 pages. arXiv admin note: text overlap with arXiv:1501.05094

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Cited by in corpus (6)

• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}{A}_{2,2}$
• On orbifold constructions associated with the Leech lattice vertex operator algebra
• Inertia groups and uniqueness of holomorphic vertex operator algebras
• Lattices, Vertex Algebras and Modular Categories