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Elliptic Genera and Vertex Operator Super-Algebras

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  • © 1999
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Overview

Authors:
  1. Hirotaka Tamanoi
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1704)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction and summary of results

    • Hirotaka Tamanoi
    Pages 1-21
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  3. Elliptic genera

    • Hirotaka Tamanoi
    Pages 22-48
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  4. Vertex operator super algebras

    • Hirotaka Tamanoi
    Pages 49-92
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  5. G-invariant vertex operator super subalgebras

    • Hirotaka Tamanoi
    Pages 93-221
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  6. Geometric structure in vector spaces and reduction of structure groups on manifolds

    • Hirotaka Tamanoi
    Pages 222-302
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  7. Infinite dimensional symmetries in elliptic genera for Kähler manifolds

    • Hirotaka Tamanoi
    Pages 303-378
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  8. Back Matter

    Pages 379-390
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Keywords

About this book

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.

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