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

Abstract

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 vertex operator algebras, generalising the classification of the Niemeier lattices by their hole diagrams.

28 pages, LaTeX; improvements to the exposition; added program code as ancillary files; to appear in Algebra Number Theory. arXiv admin note: text overlap with arXiv:2005.12248

References in corpus (1)

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

Cited by in corpus (1)

• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24