Automorphic Forms and Lie Superalgebras

  • Urmie Ray

Part of the Algebra and Applications book series (AA, volume 5)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Urmie Ray
    Pages 1-11
  3. Urmie Ray
    Pages 129-176
  4. Urmie Ray
    Pages 177-238
  5. Back Matter
    Pages 239-286

About this book

Introduction

A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice; and has an associated automorphic form having a product expansion describing its structure. Lie superalgebras are generalizations of Lie algebras, useful for depicting supersymmetry – the symmetry relating fermions and bosons. Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26.

The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course. The necessary background is given within chapters or in appendices.

Keywords

Brandonwiskunde Lattice Lie algebra algebra ring theory

Authors and affiliations

  • Urmie Ray
    • 1
  1. 1.Université de ReimsReimsFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-5010-7
  • Copyright Information Springer 2006
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4020-5009-1
  • Online ISBN 978-1-4020-5010-7
  • About this book