Inertia groups and uniqueness of holomorphic vertex operator algebras

Abstract

We continue our program on classification of holomorphic vertex operator algebras of central charge $24$. In this article, we show that there exists a unique strongly regular holomorphic VOA of central charge $24$, up to isomorphism, if its weight one Lie algebra has the type $C_{4,10}$, $D_{7,3}{A}_{3,1}{G}_{2,1}$, $A_{5,6}{C}_{2,3}{A}_{1,2}$, $A_{3,1}{C}_{7,2}$, $D_{5,4}{C}_{3,2}{A}_{1,1}^2$, or $E_{6,4}{C}_{2,1}{A}_{2,1}$. As a consequence, we have verified that the isomorphism class of a strongly regular holomorphic vertex operator algebra of central charge $24$ is determined by its weight one Lie algebra structure if the weight one subspace is nonzero.

arXiv comment46 pages

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Cited by in corpus (2)

• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions