## 9 Citations

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 $V_1$ as cyclic orbifold…

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…

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

- Mathematics
- 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…

A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra

- Mathematics
- 2022

We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA V Λ . We show that a generalized deep hole deﬁnes a “true” automorphism invariant deep hole of the…

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…

Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries

- Mathematics
- 2021

We determine the automorphism groups of the cyclic orbifold vertex operator algebras associated with coinvariant lattices of isometries of the Leech lattice in the conjugacy classes 4C, 6E, 6G, 8E…

Holomorphic integer graded vertex superalgebras

- Mathematics
- 2021

In this note we study holomorphic Z-graded vertex superalgebras. We prove that all such vertex superalgebras of central charge 8 and 16 are purely even. For the case of central charge 24 we prove…

Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra

- MathematicsJournal of Algebra
- 2021

## References

SHOWING 1-10 OF 58 REFERENCES

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…

Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

- Mathematics
- 2017

We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order $n$ such that $\Gamma_0(n)$ is a genus zero group. We then use this formula together…

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…

Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine

- Mathematics
- 1997

Abstract: The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of the theory of rational orbifold models in conformal field theory, in other words the…

$${C_2}$$C2 -Cofiniteness of Cyclic-Orbifold Models

- Mathematics
- 2015

We prove an orbifold conjecture for conformal field theory with a solvable automorphism group. Namely, we show that if V is a $${C_2}$$C2 -cofinite simple vertex operator algebra and G is a finite…

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…

Vertex algebras, Kac-Moody algebras, and the Monster.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1986

An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}A_{2,2}$

- Mathematics
- 2016

In this paper, a holomorphic vertex operator algebra $U$ of central charge 24 with the weight one Lie algebra $A_{8,3}A_{2,1}^2$ is proved to be unique. Moreover, a holomorphic vertex operator…

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…

Regularity of fixed-point vertex operator subalgebras

- Mathematics
- 2016

We show that if $T$ is a simple non-negatively graded regular vertex operator algebra with a nonsingular invariant bilinear form and $\sigma$ is a finite order automorphism of $T$, then the…