A characterization of vertex operator algebras $V_{Z\alpha}^{+}$: I
  A characterization of vertex operator algebra V_{Z\alpha}^+ with (\alpha,\alpha)/2 not being a perfect square is given in terms of dimensions of homogeneous subspaces of small weights. This result contributes to the classification of rational vertex operator algebras of central charge 1. 
Chongying Dong and Cuipo Jiang
math.QA