# 51 constructions of the Moonshine module

```@article{Carnahan201751CO,
title={51 constructions of the Moonshine module},
author={Scott Carnahan},
journal={arXiv: Representation Theory},
year={2017}
}```
We show using Borcherds products that for any fixed-point free automorphism of the Leech lattice satisfying a "no massless states" condition, the corresponding cyclic orbifold of the Leech lattice vertex operator algebra is isomorphic to the Monster vertex operator algebra. This induces an "orbifold duality" bijection between algebraic conjugacy classes of fixed-point free automorphisms of the Leech lattice satisfying this condition and algebraic conjugacy classes of non-Fricke elements in the… Expand
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 V1 as cyclic orbifoldExpand
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 orbifoldExpand
Characterizing moonshine functions by vertex-operator-algebraic conditions
• Mathematics
• 2017
Given a holomorphic \$C_2\$-cofinite vertex operator algebra \$V\$ with graded dimension \$j-744\$, Borcherds's proof of the Monstrous Moonshine Conjecture implies any finite order automorphism of \$V\$ hasExpand
Duality defect of the monster CFT
• Physics, Mathematics
• 2019
We show that the fermionization of the Monster CFT with respect to Z2A is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that theExpand
A Self-Dual Integral Form of the Moonshine Module
• Scott Carnahan
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications
• 2019
We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolvesExpand
Four self-dual integral forms of the moonshine module
We give four constructions of self-dual integral forms of the moonshine vertex operator algebra, each of which has symmetries given by the Fischer-Griess monster simple group. The existence of theseExpand
Monstrous Moonshine over the integers
Monstrous moonshine began in 1978 with a numerical observation by McKay relating representations of the monster simple group with coefficients of the modular J function. This observation initiallyExpand
A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine
Moonshine arose in the 1970s as a collection of coincidences connecting modular functions to the monster simple group, which was newly discovered at that time. The effort to elucidate theseExpand
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\$ ofExpand

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