The extensions of $L_{s{l}_2}(k,0)$ and preunitary vertex operator algebra with central charges $c<1$

The extensions of the affine vertex operator algebras $L_{s{l}_2}(k,0)$ and the preunitary vertex operator algebras with central charges $c<1$ are classified. In particular, the unitary vertex operator algebras with central charges $c<1$ are classified.