Abstract:
Let q=|q|eiπθ be a nonzero complex number such that |q|≠1 and consider the compact quantum group Uq(2). For θ∉Q∖{0,1}, we obtain the K-theory of the underlying C⁎-algebra C(Uq(2)). We construct a spectral triple on Uq(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 Uq(2). The K-homology class of the associated Fredholm module is shown to be nontrivial.