Introduction to vertex operator algebras III
Abstract
This is the third part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and YiZhi Huang in the conference on Monster and vertex operator algebras at the Research Institute of Mathematical Sciences, Kyoto, September 49, 1994. In this part, we discuss an $S_{3}$symmetry of the Jacobi identity, construct the contragredient module for a module for a vertex operator algebra and apply these to the construction of the vertex operator map for the moonshine module. We review the notions of intertwining operator, fusion rule and Verlinde algebra. We also describe briefly the geometric interpretation of vertex operator algebras. We end the exposition with an explanation of the role of vertex operator algebras in conformal field theories.
 Publication:

eprint arXiv:qalg/950401
 Pub Date:
 April 1995
 arXiv:
 arXiv:qalg/9504019
 Bibcode:
 1995q.alg.....4019H
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 AMSLaTeX file, 28 pages