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Elliptic Genera and Vertex Operator Super-Algebras

  • Authors
  • Hirotaka Tamanoi

Part of the Lecture Notes in Mathematics book series (LNM, volume 1704)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Hirotaka Tamanoi
    Pages 1-21
  3. Hirotaka Tamanoi
    Pages 22-48
  4. Hirotaka Tamanoi
    Pages 49-92
  5. Hirotaka Tamanoi
    Pages 93-221
  6. Back Matter
    Pages 379-390

About this book

Introduction

This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.

Keywords

Kähler manifolds Spin representations Vector space Virasoro algebras affine Lie algebras algebra modular functions super algebras vertex operator

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092541
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66006-4
  • Online ISBN 978-3-540-48788-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site