Inductions and coinductions for Hopf extensions
When \(H\) is a finite dimensional Hopf algebra, the concept of \(H\)-Galois extensions for \(H\)-comodule algebras has a dual in terms of \(H\)-modules \(A\); this involves the surjectivity of the Morita maps for \(A\), \(A\#H\) and \(A^{\text{co}H}\). The authors study induction and coinduction functors for both types of extensions. The paper gives (for example) a functorial characterization of Hopf extensions with elements of trace 1: such an element exists if and only if the induced and coinduced functors from the Hopf module category to the invariant module category are isomorphic. They also prove that some of the good properties of Hopf Galois extensions are in fact separability conditions on suitable functors.
functorial characterization of Hopf extensions
scientific article; zbMATH DE number 908302