Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Group of Symmetries of the shorter Moonshine Module

Gerald Höhn

TL;DR

This note proves that the automorphism group of the shorter Moonshine module VB^natural is the direct product of the Baby Monster and a cyclic group of order 2. It identifies the Baby Monster with the automorphism group of the weight-2 subspace via Miyamoto involutions associated to 2A and 2B axes and shows the even part VB^natural_(0) is generated by that weight-2 subspace using framed VOA techniques. The argument uses the Moonshine module V^natural, the Griess algebra, and centralizer structures in the Monster to determine the full symmetry group of the associated superalgebra, illustrating a VOA-based symmetry realization of sporadic groups.

Abstract

It is shown that the automorphism group of the shorter Moonshine module constructed in my Ph.D. thesis (also called Baby Monster vertex operator superalgebra) is the direct product of the finite simple group known as the Baby Monster and the cyclic group of order 2.

The Group of Symmetries of the shorter Moonshine Module

TL;DR

This note proves that the automorphism group of the shorter Moonshine module VB^natural is the direct product of the Baby Monster and a cyclic group of order 2. It identifies the Baby Monster with the automorphism group of the weight-2 subspace via Miyamoto involutions associated to 2A and 2B axes and shows the even part VB^natural_(0) is generated by that weight-2 subspace using framed VOA techniques. The argument uses the Moonshine module V^natural, the Griess algebra, and centralizer structures in the Monster to determine the full symmetry group of the associated superalgebra, illustrating a VOA-based symmetry realization of sporadic groups.

Abstract

It is shown that the automorphism group of the shorter Moonshine module constructed in my Ph.D. thesis (also called Baby Monster vertex operator superalgebra) is the direct product of the finite simple group known as the Baby Monster and the cyclic group of order 2.

Paper Structure

This paper contains 2 sections, 6 theorems, 6 equations, 1 table.

Table of Contents

  1. Introduction
  2. Proof of Theorem

Key Result

Theorem 1

The automorphism group of the shorter Moonshine module $V\!B^{\natural}$ is the direct product of the Baby Monster ${\mathbb B}$ and a cyclic group of order $2$.

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Lemma 3
  • Lemma 4
  • Proposition 5
  • Proposition 6