# 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…

## References

SHOWING 1-10 OF 74 REFERENCES

Holomorphic vertex operator algebras of small central charge

- Mathematics
- 2002

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we…

Construction and classification of holomorphic vertex operator algebras

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2020

Abstract We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of V1{V_{1}}-structures of meromorphic…

Rational vertex operator algebras and the effective central charge

- Mathematics
- 2002

We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c~. We…

Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra

- Mathematics
- 2019

We prove a dimension formula for the weight-1 subspace of a vertex operator algebra $V^{\operatorname{orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra $V$ of…

A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications

- Mathematics
- 2016

In this thesis we develop an orbifold theory for a finite, cyclic group $G$ acting on a suitably regular, holomorphic vertex operator algebra $V$. To this end we describe the fusion algebra of the…

On orbifold constructions associated with the Leech lattice vertex operator algebra

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2018

Abstract In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic…

Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices

- Mathematics
- 2020

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras V of central charge 24 with non-zero weight-one space V1 as cyclic orbifold…

Vertex operator algebras associated to representations of affine and Virasoro Algebras

- Mathematics
- 1992

The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formula…