On classification of rational vertex operator algebras with central charges less than 1

The rational and C-2-cofinite simple vertex operator algebras whose effective central charges c and the central charges c are equal and less than I are classified. Such a vertex operator algebra is zero if (c) over tilde < 0 and C if <(c)over tilde> = 0. If (c) over tilde > 0, it is an extension of discrete Virasoro vertex operator algebra L(c(p,q), 0) by its irreducible modules. It is also proved that for any rational and C-2-cofinite simple vertex operator algebra with c = (c) over tilde, the vertex operator subalgebra generated by the Virasoro vector is simple. (C) 2007 Elsevier Inc. All rights reserved.