On Frobenius extensions defined by Hopf algebras (Q1330081)

It is well known that finite dimensional Hopf algebras \(H\) are Frobenius algebras. Thus they possess a Nakayama automorphism which is investigated in this paper. The author shows that \(H\) is unimodular iff \(S^ 2\) is a Nakayama automorphism (where \(S\) is the antipode of \(H\)). \(H\) is symmetric iff \(H\) is unimodular and \(S^ 2\) is an inner automorphism. Other interesting results concern the freeness of a Hopf algebra \(H\) over a subalgebra \(B\). The author proves that \(H : B\) is free if \(B\) is generated by group-like and primitive elements.