We continue studying normal left coideal subalgebras of a Hopf algebra
realizing them as invariants of
under the left hit action of Hopf subalgebras of
We apply this realization to test an equivalence relation on irreducible characters for two important examples. The commutator sublagebra of
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
where commutators are computed.