Non-commutative phase and the unitarization of GL_{p,q}(2)
  In this paper, imposing hermitian conjugate relations on the two-parameter deformed quantum group GL_{p,q}(2) is studied. This results in a non-commutative phase associated with the unitarization of the quantum group. After the achievement of the quantum group U_{p,q}(2) with pq real via a non-commutative phase, the representation of the algebra is built by means of the action of the operators constituting the U_{p,q}(2) matrix on states. 
Metin Arik, Burak T. Kaynak