On normal Hopf subalgebras of semisimple Hopf algebras. (Q421489)

Suppose that \(H\) is a finite-dimensional Hopf algebra over an algebraically closed field and \(C(H) \) is its character ring. Let \(C\) be a subcoalgebra in \(H\). There is given a criterion in terms of centrality of its characters under which \(C\) is invariant under the adjoint action of \(H\) on \(C\). If \(K\) is a normal Hopf subalgebra in \(H\) then the restriction functor defines an algebra map \(\text{res}^H_K\colon C(H)\to C(K)\) and the induction functor \(\text{ind}^H_K\colon C(K)\to C(H)\). Then the image of \(\text{ind}^H_K\) coincides with the set of elements \(\chi\in C(H)\) such that \(\sum_aa_{(1)}\chi(S(a_{(2)})\in K\) for all \(a\in H\). In a similar way there is given an algebra generating set of the image of \(\text{res}^H_K\).