Quantum GL(2, C) group as double group over ‘az + b’ quantum group

In this paper the quantum GL(2, C) group constructed in [4] is investigated. The deformation parameter q = e2πeN, where N is an even natural number. It is shown that this group can be obtained by the double group construction applied to the quantum ‘az + b’ group. The latter is the quantum deformation of the group of affine transformations of complex plane introduced in [9].