# A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24

@inproceedings{Mller2021AGC, title={A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24}, author={Sven Karup M{\o}ller and Nils R. Scheithauer}, year={2021} }

We associate with a generalised deep hole of the Leech lattice vertex operator algebra a generalised hole diagram. We show that this Dynkin diagram determines the generalised deep hole up to conjugacy and that there are exactly 70 such diagrams. In an earlier work we proved a bijection between the generalised deep holes and the strongly rational, holomorphic vertex operator algebras of central charge 24 with non-trivial weight-1 space. Hence, we obtain a new, geometric classification of these…

## One Citation

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

- Mathematics
- 2022

. 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…

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