Construction of Families of Vertex Operator Algebras and Modules

  • James Lepowsky
  • Haisheng Li
Part of the Progress in Mathematics book series (PM, volume 227)


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.


Vertex Operator Central Extension Vertex Operator Algebra Vertex Algebra Irreducible Module 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • James Lepowsky
    • 1
  • Haisheng Li
    • 2
  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA
  2. 2.Department of MathematicsRutgers UniversityCamdenUSA

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