Construction of Families of Vertex Operator Algebras and Modules

Abstract

We have developed the fundamental theory of vertex operator algebras and, modules in Chapters 1 through 5. The reader has certainly noticed that so far we have not constructed or exhibited any examples of vertex (operator) algebras other than the vertex (operator) algebras based on commutative associative algebras. Unlike in classical algebraic theories such as the theory of Lie or associative algebras, nontrivial examples of vertex (operator) algebras and, modules for them cannot be easily presented right after the definitions. But now, with the general representation theory having been developed in Chapter 5, we are fully prepared to present an array of interesting examples of vertex operator algebras and, modules, by systematically invoking this general representation theory.KeywordsVertex OperatorCentral ExtensionVertex Operator AlgebraVertex AlgebraIrreducible ModuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.