Elliptic Genera and Vertex Operator Super-Algebras

• Main Author: Tamanoi, Hirotaka (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1704
• Subjects: Algebra.; Algebraic topology.; Nonassociative rings.; Rings (Algebra).; Mathematical physics.; Algebraic Topology.; Non-associative Rings and Algebras.; Theoretical, Mathematical and Computational Physics.
• Physical Description: VIII, 396 p. online resource.
• ISBN: 9783540487883
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0092541

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.