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arXiv · 2203.15992

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

Koichi Betsumiya·Ching Hung Lam·Hiroki Shimakura
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Abstract

We describe the automorphism groups of all holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one Lie algebras by using their constructions as simple current extensions. We also confirm a conjecture of G. H\"ohn on the numbers of holomorphic vertex operator algebras of central charge $24$ obtained as inequivalent simple current extensions of certain vertex operator algebras, which gives another proof of the uniqueness of holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one Lie algebras.

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Koichi Betsumiya, Ching Hung Lam, Hiroki Shimakura. 2022-03-30. Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$. https://doi.org/10.1007/s00220-022-04585-6

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