Inertia groups and uniqueness of holomorphic vertex operator algebras

2018/04/07 by Lam, Ching Hung, Shimakura, Hiroki
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/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_7,3A_3,1G_2,1, A_5,6C_2,3A_1,2, A_3,1C_7,2, D_5,4C_3,2A_1,1², or E_6,4C_2,1A_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.

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