Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras

Hopf Galois extensions, triangular structures, and Frobenius Lie algebras in prime characteristic

“…The next proposition restates several facts from [8,Th. 3.4], with H and H * interchanged by our conventions.…”

“…This is again just a special case of results in [46], [8]. A direct argument based on Lemma 3.2 runs as follows.…”

“…Given an H-Galois algebra, there is a canonically defined right action of H on the algebra under consideration [46], [8]. The next proposition restates several facts from [8,Th.…”

“…The H * -comodule structure on A is given by the map a → h i a ⊗ h * i . Hence (3.1) is exactly the exchange rule from [46], [8]. The symmetry between H and H * is apparent in (3.1).…”

“…Category equivalences in more general settings are described in [6], [7], [8], [40], [46]. Corollary 1.3.…”