Geometrically reductive Hopf algebras. II (Q1339998)

In this paper the study of part I [\textit{H. Borsari} and the author, ibid. 152, No. 1, 65-77 (1992; Zbl 0803.16038)] is restricted to finite dimensional commutative Hopf algebras \(C\) which are shown to be geometrically reductive. In characteristic \(p\) the exponent of \(C\) is a \(p\)-th power dividing \(\dim (C)\). A version of Maschke's theorem follows: \(C\) is a direct sum of subcoalgebras if the characteristic is zero or does not divide \(\dim(C)\). The theory of Frobenius kernels is revisited.