On classification 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 and C if . If , 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 , the vertex operator subalgebra generated by the Virasoro vector is simple.