Analysis on a Homogeneous Space of a Quantum Group
  A detailed account of the construction of a homogeneous space for the quantum "az+b" group is presented. The homogeneous space is described by a commutative C*-algebra which means that it is a classical space. Then a covariant differential calculus on the homogeneous space is constructed and studied. A covariant measure and an analogue of the exponential function are used to introduce elements of Fourier analysis. 
W. Pusz, P. M. So{\l}tan