A characteristic map for compact quantum groups

We show that if G is a compact Lie group and g is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra U q ( g ) to the twisted cyclic cohomology of quantum group algebra O ( G q ) . We also show that the Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podleś sphere O ( S q 2 ) is in the image of this map.