Trace-like functionals on the double of the Taft Hopf algebra

The cocommutative elements of the dual of the double D∗(H), which are the trace-like functionals on D(H), of the Taft (Hopf) algebra H over a field k are studied in detail. The subalgebra of cocommutative elements of D∗(H) is isomorphic to the center of D(H). Trace-like functionals on D(H) determine regular isotopy invariants of oriented knots and links. Specific calculations made here suggest that further study of these invariants is definitely warranted.