71 holomorphic vertex operator algebras of central charge 24

Abstract

In this article, we give a survey on the recent progress towards the classification of strongly regular holomorphic vertex operator algebras of central charge 24. In particular, we review the construction of the holomorphic vertex operator algebras that realize the 71 Lie algebras in Schellekens’ list. In addition, we discuss an open question if the Lie algebra structure of the weight one subspace will determine the isomorphism class of a holomorphic vertex operator algebra of central charge 24 uniquely.