We discuss the non-Hermitian realization of a Lie-deformed, non-canonical Heisenberg algebra. We show that it essentially amounts to the case of a Q-deformed algebra with complex deformation parameter. The (real) energy eigenvalues of the corresponding oscillator are derived, whose deformed spectrum has, among the others, a ground state energy lower than that of the usual harmonic oscillator. The non-Hermitian deformed SU(2) algebra is also constructed.
Jannussis, A., Leodaris, A., Mignani, R. (1995). NON-HERMITIAN REALIZATION OF A LIE-DEFORMED HEISENBERG ALGEBRA. PHYSICS LETTERS A, 197(3), 187-191 [10.1016/0375-9601(94)00968-U].