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.

Bibliographic Information

Book Title: Elliptic Genera and Vertex Operator Super-Algebras
Authors: Hirotaka Tamanoi
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0092541
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1999
Softcover ISBN: 978-3-540-66006-4Published: 21 June 1999
eBook ISBN: 978-3-540-48788-3Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 396
Topics: Algebra, Algebraic Topology, Non-associative Rings and Algebras, Theoretical, Mathematical and Computational Physics

Publish with us

Policies and ethics

Elliptic Genera and Vertex Operator Super-Algebras

Overview

Access this book

Other ways to access

Table of contents (6 chapters)

Front Matter

Introduction and summary of results

Elliptic genera

Vertex operator super algebras

G-invariant vertex operator super subalgebras

Geometric structure in vector spaces and reduction of structure groups on manifolds

Infinite dimensional symmetries in elliptic genera for Kähler manifolds

Back Matter

Keywords

About this book

Bibliographic Information

Publish with us

Search

Navigation