Elliptic genera and vertex operator super-algebras / Hirotaka Tamanoi
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1704Langue : anglais.Éditeur : Berlin : Springer, 1999ISBN: 9783540660064.ISSN: 1617-9692.Sujet MSC : 17B69, Lie algebras and Lie superalgebras, Vertex operators; vertex operator algebras and related structures58J26, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Elliptic genera
17A70, General nonassociative rings, Superalgebras
81R10, Groups and algebras in quantum theory, Infinite-dimensional groups and algebras motivated by physics
17B68, Lie algebras and Lie superalgebras, Virasoro and related algebrasEn-ligne : Springerlink | Zentralblatt | MathScinet
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 mainly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras. (Zentralblatt)
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