Hopf extensions of algebras and Maschke type theorems
Let A be a Hopf algebra. An A-extension B/C is an A-comodule algebra B with invariant subalgebra C. An (A,B)-Hopf module is an A-comodule and a B-module such that the comodule structure map is a B-module homomorphism. The paper gives sufficient conditions (1) that B/C is an A-Galois extension, (2) that A-Galois extensions are separable, (3) that exact sequences of B-modules which split as C-modules also split as B-modules, (4) that exact sequences of (A,B)-Hopf modules which split as B-modules also split as (A,B)-Hopf modules, (5) that B is semisimple artinian and (6) that B is a C-Frobenius extension.
scientific article; zbMATH DE number 4208319