Inertia groups and uniqueness of holomorphic vertex operator algebras

Ching Hung Lam; Hiroki Shimakura

paper

Inertia groups and uniqueness of holomorphic vertex operator algebras

arXiv:1804.02521

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.

46 pages