A correspondence between homogeneous and Galois coactions of Hopf algebras (Q2199641)

Let \(H\) be a Hopf algebra and let \(A\) be a unital \(H\)-comodule algebra. It is \textit{homogeneous} if its space of coinvariants is reduced to the base field, and it is a \textit{partial Galois object} if \(A\) is Galois and if its space of coinvariants is reduced to a direct sum of copies of the base field. A one-to-one correspondence is defined between, on one hand, semisimple homogeneous \(H\)-comodules algebras up to Morita equivalence, and, on the other hand, connected partial Galois objects up to comodule-algebra isomorphisms. As corollaries, results on the structure of partial Galois objects are given: existence of invariant functionals and of a Nakayama automorphism.