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

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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 c<0 and C if c=0. If c>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 whose effective central charge and central charge are equal, the vertex operator subalgebra generated by the Virasoro vector is simple.