Stereographic coordinates for unitary quantum groups - Arıkan, Ali Serdar. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998)
In this thesis, unitary matrix representation of quantum group SUq(2) is studied in terms of stereographic coordinates z, z* and its central unitary phase u. It is observed that this parametrization of SUq(2) can be regarded as q-1-oscillator representation of SUq(2) where q-1>1. The fractional linear transformation of z and z* which gives the action of SUq(2) on the quantum sphere SUq(2)/U(1) is studied. Then we extend this action to SUq(2) and derive the transformation law of u. In the final part of this work, transformation laws for dz and are also studied.
Keywords: Unitary groups.; Quantum theory.