Introduction to Vertex Operator Algebras and Their Representations [electronic resource] /

1 Introduction -- 1.1 Motivation -- 1.2 Example of a vertex operator -- 1.3 The notion of vertex operator algebra -- 1.4 Simplification of the definition -- 1.5 Representations and modules -- 1.6 Construction of families of examples -- 1.7 Some further developments -- 2 Formal Calculus -- 2.1 Formal series and the formal delta function -- 2.2 Derivations and the formal Taylor Theorem -- 2.3 Expansions of zero and applications -- 3 Vertex Operator Algebras: The Axiomatic Basics -- 3.1 Definitions and some fundamental properties -- 3.2 Commutativity properties -- 3.3 Associativity properties -- 3.4 The Jacobi identity from commutativity and associativity -- 3.5 The Jacobi identity from commutativity -- 3.6 The Jacobi identity from skew symmetry and associativity -- 3.7 S3-symmetry of the Jacobi identity -- 3.8 The iterate formula and normal-ordered products -- 3.9 Further elementary notions -- 3.10 Weak nilpotence and nilpotence -- 3.11 Centralizers and the center -- 3.12 Direct product and tensor product vertex algebras -- 4 Modules -- 4.1 Definition and some consequences -- 4.2 Commutativity properties -- 4.3 Associativity properties -- 4.4 The Jacobi identity as a consequence of associativity and commutativity properties -- 4.5 Further elementary notions -- 4.6 Tensor product modules for tensor product vertex algebras -- 4.7 Vacuum-like vectors -- 4.8 Adjoining a module to a vertex algebra -- 5 Representations of Vertex Algebras and the Construction of Vertex Algebras and Modules -- 5.1 Weak vertex operators -- 5.2 The action of weak vertex operators on the space of weak vertex operators -- 5.3 The canonical weak vertex algebra ?(W) and the equivalence between modules and representations -- 5.4 Subalgebras of ?(W) -- 5.5 Local subalgebras and vertex subalgebras of ?(W) -- 5.6 Vertex subalgebras of ?(W) associated with the Virasoro algebra -- 5.7 General construction theorems for vertex algebras and modules -- 6 Construction of Families of Vertex Operator Algebras and Modules -- 6.1 Vertex operator algebras and modules associated to the Virasoro algebra -- 6.2 Vertex operator algebras and modules associated to affine Lie algebras -- 6.3 Vertex operator algebras and modules associated to Heisenberg algebras -- 6.4 Vertex operator algebras and modules associated to even lattices—the setting -- 6.5 Vertex operator algebras and modules associated to even lattices—the main results -- 6.6 Classification of the irreducible L?(?, O)-modules for g finite-dimensional simple and ? a positive integer -- References.

Bibliographic Details

Main Authors:	Lepowsky, James. author., Li, Haisheng. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2004
Subjects:	Mathematics., Algebra., Associative rings., Rings (Algebra)., Topological groups., Lie groups., Operator theory., Physics., Associative Rings and Algebras., Operator Theory., Topological Groups, Lie Groups., Theoretical, Mathematical and Computational Physics.,
Online Access:	http://dx.doi.org/10.1007/978-0-8176-8186-9
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