Abstract
We consider a Hopf Galois extension B A, for A a comodule algebra over the Hopf algebra H with coinvariant algebra B . After giving a number of examples, we discuss Galois extensions with additional properties, such as having a normal basis. We then consider when there is a category equivalence between the category of modules over B and the category of “relative Hopf modules” for A and H . Finally we discuss more recent work of van Oystaeyen and Zhang and of Schauenburg on obtaining correspondence theorems between suitable subalgebras of A and Hopf ideals of H . 16W30; 16S40, 16S34
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