A Two-Parameter Quantum Deformation of the Unit Disc

We define and study a two-parameter deformation of the unit disc. This deformation is described in terms of a family of type I C-algebras Cμ,q(Ū). We study the representation theory for Cμq(Ū) and construct an action of the quantized universal enveloping algebra Uq(sl(2)) on Cμq(Ū).