Abstract

In 1993, Schellekens obtained a list of possible Lie algebra structures for the weight one subspaces of holomorphic vertex operator algebras (VOA) of central charge 24. It was also conjectured that the VOA structure of a holomorphic VOA of central charge 24 is uniquely determined by the Lie algebra structure of its weight one space. Recently, all 71 cases in Schellekens' list have been constructed.  

In this talk, we will discuss the recent progress on the classification of holomorphic vertex operator algebras of central charge 24. In particular, we will discuss the construction of holomorphic VOAs using various types of orbifold constructions. A technique, which we call ``Reverse orbifold construction”, will also be discussed. This technique may be used to prove the uniqueness of holomorphic VOAs of central charge 24 if the weight one subspace is not zero.