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Representations of vertex operator algebras

Chongying Dong·Cuipo Jiang
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Abstract

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is a semisimple associative algebra and each irreducible admissible $V$-module is ordinary.

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Chongying Dong, Cuipo Jiang. 2006-07-09. Representations of vertex operator algebras. https://arxiv.org/abs/math/0603588

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