# Monstrous Moonshine over Z

@article{Carnahan2018MonstrousMO, title={Monstrous Moonshine over Z}, author={Scott Carnahan}, journal={arXiv: Representation Theory}, year={2018} }

Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine conjecture. Both conjectures have been unconditionally resolved in the last few years, so we describe some speculative conjectures that may extend and unify them.

## 2 Citations

Snowmass White Paper: Moonshine

- Mathematics
- 2022

We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex…

## References

SHOWING 1-10 OF 32 REFERENCES

Monstrous moonshine and monstrous Lie superalgebras

- Mathematics
- 1992

We prove Conway and Norton's moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by Frenkel, Lepowsky and Meurman. To do this we use the no-ghost…

Four self-dual integral forms of the moonshine module

- Mathematics
- 2017

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 these…

On the relationship between Monstrous Moonshine and the uniqueness of the Moonshine Module

- Mathematics
- 1995

We consider the relationship between the conjectured uniqueness of the Moonshine Module,, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group…

Generalised Moonshine and Holomorphic Orbifolds

- Mathematics
- 2013

Generalised moonshine is reviewed from the point of view of holomorphic orbifolds, putting special emphasis on the role of the third cohomology group H^3(G, U(1)) in characterising consistent…

Beauty and the beast: Superconformal symmetry in a monster module

- Mathematics
- 1988

Frenkel, Lepowsky, and Meurman have constructed a representation of the largest sporadic simple finite group, the Fischer-Griess monster, as the automorphism group of the operator product algebra of…

The fake monster formal group

- Mathematics
- 1998

The main result of this paper is the construction of ``good'' integral forms for the universal enveloping algebras of the fake monster Lie algebra and the Virasoro algebra. As an application we…

Generalized moonshine, II: Borcherds products

- Mathematics
- 2012

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of…

Generalized moonshine I: Genus-zero functions

- Mathematics
- 2010

We introduce a notion of Hecke-monicity for functions on certain moduli spaces associated to torsors of finite groups over elliptic curves, and show that it implies strong invariance properties under…

BPS algebras, genus zero and the heterotic Monster

- Mathematics
- 2017

In this note, we expand on some technical issues raised in (Paquette et al 2016 Commun. Number Theory Phys. 10 433-526) by the authors, as well as providing a friendly introduction to and summary of…

CLASSIFYING SPACES, VIRASORO EQUIVARIANT BUNDLES, ELLIPTIC COHOMOLOGY AND MOONSHINE

- Mathematics
- 2013

This work explores some connections between the elliptic cohomology of classifying spaces for finite groups, Virasoro equivariant bundles over their loop spaces and Moonshine for finite groups. Our…