Fusion rules of Virasoro vertex operator algebras

Abstract

In this paper we prove the fusion rules of Virasoro vertex operator algebras $L(c_{1,q},0)$, for $q\geq 1$. Roughly speaking, we consider $L(c_{1,q},0)$ as the limit of $L(c_{n,nq-1},0)$, for $n\rightarrow \infty$, and the fusion rules of $L(c_{1,q},0)$ follow as the limits of the fusion rules of $L(c_{n,nq-1},0)$.