Hit-invariants and commutators for Hopf algebras

We continue studying normal left coideal subalgebras of a Hopf algebra H, realizing them as invariants of H under the left hit action of Hopf subalgebras of H*. We apply this realization to test an equivalence relation on irreducible characters for two important examples. The commutator sublagebra of H, which is the analogue of the commutator subgroup of a group and the image of the Drinfeld map for quasitriangular Hopf algebras. We end with the example H = D(kS(3)) where commutators are computed.