Some Finiteness Properties of Regular Vertex Operator Algebras

Abstract

We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu'sC2-finiteness condition holds, fusion rules (for any three irreducible modules) are finite and the vertex operator algebras themselves are finitely generated. © 1999 Academic Press.