Abstract

A holomorphic vertex operator algebra (VOA) is a simple -cofinite rational VOA with a unique irreducible module up to the isomorphisms. An example of the holomorphic VOAs is the moonshine VOA of central charge , whose automorphism group is the Fischer-Griess monster group and character is , where is the -function. It has been conjectured that there are exactly holomorphic VOAs of central charge and they are uniquely determined by their associated Lie algebras. They have recently been studied extensively and the existence of holomorphic VOAs was proved by combining many studies by various researchers. Moreover, several holomorphic VOAs of central charge were proved to be determined by their associated Lie algebras.

In this talk, I will explain basics of VOAs and provide a new result that a class of holomorphic VOAs of central charge are determined by their associated Lie algebras.

This is a joint work with Ching Hung Lam and Xingjun Lin.