Introduction to vertex operator algebras III

Details Introduction to vertex operator algebras III Introduction to vertex operator algebras III

1995-04-24

arxiv.org/abs/q-alg/9504019v1

Physics

High Energy Physics

High Energy Physics - Theory

AMS-LaTeX file, 28 pages

Scientific paper

This is the third part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute of Mathematical Sciences, Kyoto, September 4-9, 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.

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