The Virasoro Algebra and Some Exceptional Lie and Finite Groups

Abstract

We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.

Keywords

• vertex operator algebras
• Virasoro algebras
• Deligne exceptional series
• Monster group