On Axiomatic Approaches To Vertex Operator Algebras And Modules
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On Axiomatic Approaches to Vertex Operator Algebras and Modules
Author: Igor Frenkel
language: en
Publisher: Oxford University Press, USA
Release Date: 2014-08-31
The notion of vertex operator algebra arises naturally in the vertex operator construction of the Monster---the largest sporadic finite simple group. From another perspective, the theory of vertex operator algebras and their modules forms the algebraic foundation of conformal field theory. Vertex operator algebras and conformal field theory are now known to be deeply related to many important areas of mathematics. This essentially self-contained monograph develops the basic axiomatic theory of vertex operator algebras and their modules and intertwining operators, following a fundamental analogy with Lie algebra theory. The main axiom, the Jacobi(-Cauchy) identity'', is a far-reaching analog of the Jacobi identity for Lie algebras. The authors show that the Jacobi identity is equivalent to suitably formulated rationality, commutativity, and associativity properties of products of quantum fields. A number of other foundational and useful results are also developed.
On Axiomatic Approaches to Vertex Operator Algebras and Modules
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.
Introduction to Vertex Operator Algebras and Their Representations
Author: James Lepowsky
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.