Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C)   approach
  Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A$_1$. 
B. Bagchi, C. Quesne