Toward classfication of rational vertex operator algebras with central charges less than 1

The rational and C2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c̃ < 0 and C if c̃ = 0. If c̃ > 0, it is an extension of discrete Virasoro vertex operator algebra L(cp,q, 0) by its irreducible modules. It is also proved that for any rational and C2-cofinite simple vertex operator algebra with c = c̃, the vertex operator subalgebra generated by the Virasoro vector is simple.