The extensions of $L_{sl_2}(k,0)$ and preunitary vertex operator algebra   with central charges $c<1$
  The extensions of the affine vertex operator algebras $L_{sl_2}(k,0)$ 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. 
Chongying Dong and Xingjun Lin
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