Podleś Spheres for the Braided Quantum SU(2)

Abstract Starting with the braided quantum group SU q ( 2 ) for a complex deformation parameter q we perform the construction of the quotient SU q ( 2 ) / T which serves as a model of a quantum sphere. Then we follow the reasoning of Podleś who for real q classified quantum spaces with the action of SU q ( 2 ) with appropriate spectral properties. These properties can also be expressed in the context of the braided quantum SU q ( 2 ) (with complex q) and we find that they lead to precisely the same family of quantum spaces as found by Podleś for the real parameter | q | .