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Elliptic Genera and Vertex Operator Super-Algebras : Lecture Notes in Mathematics - H. Tamanoi

Elliptic Genera and Vertex Operator Super-Algebras

Lecture Notes in Mathematics

Paperback Published: July 1999
ISBN: 9783540660064
Number Of Pages: 396

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This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, & 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 Kahler manifolds such as Riemannian tensors & Kahler forms are shown to give rise to Virasoro algebras & affine Lie algebras. This monograph is chiefly intended for topologists & it includes accounts on topics outside of topology such as vertex operator algebras.

Introduction and summary of resultsp. 1
Towards the signature of loop spaces: Elliptic genusp. 1
Elliptic generap. 4
Vertex operator super-algebrasp. 7
G-invariant vertex operator super-subalgebras and their vertex operatorsp. 9
Classifying spaces of geometric structures on manifoldsp. 13
Elliptic genera as modules over vertex operator super- algebrasp. 16
Infinite dimensional symmetries of elliptic genera for Kähler manifoldsp. 17
Elliptic generap. 22
Elliptic generap. 22
Theta functions and elliptic functionsp. 29
Proof of Theorem 4 of §1.1p. 32
The modular properties of elliptic generap. 35
On the divisibility of coefficients of the elliptic genus ϕellRp. 42
Spinors on loop spaces: the Witten genusp. 46
Vertex operator super-algebrasp. 49
Vertex operator super-algebras: A brief introductionp. 49
The infinite dimensional Clifford modules as vertex oper- ator super-algebras and their modulesp. 60
Clifford algebras, Virasoro algebras and affine Lie algebras as subalgebras of the vertex operator super-algebra Vp. 65
The adjoint operators of vertex operatorsp. 72
G-invariant vertex operator super-subalgebrasp. 93
VG as vertex operator super-algebrap. 93
Lie algebras as Lie subalgebras of Clifford algebrasp. 94
Commutants of Lie subalgebras in o(2N) and Casimir elementsp. 104
Generating G-invariant vectors in (V)*p. 111
Vertex operators associated to G-invariant vectors of low weightp. 122
Unitary Virasoro algebrasp. 129
Vertex operators generated by complex volume formsp. 139
Symplectic Virasoro algebrasp. 147
Kähler forms in quaternionic vector spacesp. 174
Unitary Virasoro algebras in quaternionic vector spacesp. 185
Vertex operators for products of Kähler forms and their commutatorsp. 188
Determination of G-invariant vectors of low weight in the vertex operator super-algebra (V )*p. 211
Geometric structures in vector spaces and reductions of structure groups on manifoldsp. 222
Some geometric structures in vector spacesp. 222
Moduli of geometric structures as G-orbits in representa- tion spaces: Some examples of interestp. 236
A general theory of geometric structures in vector spaces and their compatibilitiesp. 250
On connections and parallelismp. 268
Reductions of structure groups on manifolds and parallel sectionsp. 285
Infinite dimensional symmetries in elliptic genera for Kahler manifoldsp. 303
Kählerian manifoldsp. 303
Generalizations of Riemannian metrics, Riemannian vol- ume forms, Kähler forms, complex volume forms, and quaternion-Kähler formsp. 313
Twisted G-Dirac operatorsp. 326
Elliptic genera as modules over vertex operator super- algebras of parallel sectionsp. 337
Infinite dimensional symmetries in elliptic genera for Kahler manifoldsp. 357
Referencesp. 379
Index of Notationp. 383
Subject Indexp. 387
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540660064
ISBN-10: 3540660062
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 396
Published: July 1999
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.11
Weight (kg): 0.56

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