Computing the connes spectrum of a Hopf algebra

LetH be a finite-dimensional Hopf algebra over the fieldK and letA be anH-module algebra. In a previous paper, we defined the Connes spectrum CS(A, H) for the action ofH onA to be a certain subset of the set Irr(H) of irreducible representations ofH. In this paper, we compute a number of examples; specifically, we consider certain inner and outer actions and we take a closer look at the cocommutative situation. We discover that the information encoded in the Connes spectrum is rather subtle and elusive. Research supported in part by NSF Grant DMS-8900405.