Equivariant spectral triple for the quantum group Uq(2) for complex deformation parameters

Let q=|q|e^iπθ be a nonzero complex number such that |q|≠1 and consider the compact quantum group U<inf>q</inf>(2). For θ∉Q∖{0,1}, we obtain the K-theory of the underlying C^⁎-algebra C(U<inf>q</inf>(2)). We construct a spectral triple on U<inf>q</inf>(2) which is equivariant under its own comultiplication action. The spectral triple obtained here is even, 4⁺-summable, non-degenerate, and the Dirac operator acts on two copies of the L²-space of U<inf>q</inf>(2). The K-homology class of the associated Fredholm module is shown to be nontrivial.