Abstract
Starting with the braided quantum group SUq(2) for a complex deformation parameter q we perform the construction of the quotient SUq(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 SUq(2) with appropriate spectral properties. These properties can also be expressed in the context of the braided quantum SUq(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|.
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