sl(2, C) as a complex Lie algebra and the associated non-Hermitian   Hamiltonians with real eigenvalues
  The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C) or $A_1$. This leads to new types of both PT-symmetric and non-PT-symmetric Hamiltonians. 
B. Bagchi, C. Quesne