On the isomorphic classes of Hopf-Galois extensions with normal bases over a commutative ring (Q1819112)

Let \(H\) be a finite cocommutative Hopf algebra over a commutative ring. The authors show that the isomorphism types of \(H\)-Galois extensions with the normal basis property of a fixed commutative ring \(B\) are in bijection with the cohomology group \(H^2(L^*,U)\), where \(L=B\otimes H\) and \(L^*=\text{Hom}_B(L,B)\). Related work has been done by \textit{Y. Doi} [Commun. Algebra 17, No. 12, 3053-3085 (1989; Zbl 0687.16008)].