Pseudo-Galois Extensions and Hopf Algebroids
A pseudo-Galois extension is shown to be a depth two extension. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups, or more generally involutive Hopf algebras, and their module algebras. It is a type of cofibered sum of two inclusions of the Hopf algebra into the semi-direct product and its derived right crossed product. Van Oystaeyen and Panaite observe that this Hopf algebroid is nontrivially isomorphic to a Connes-Moscovici Hopf algebroid.
KeywordsHopf Algebra Semidirect Product Algebra Homomorphism Galois Extension Base Algebra
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