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Pseudo-Galois Extensions and Hopf Algebroids

Lars Kadison
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Abstract

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 non-trivially isomorphic to a Connes-Moscovici Hopf algebroid, which raises interesting comparative questions.

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Lars Kadison. 2006-08-21. Pseudo-Galois Extensions and Hopf Algebroids. https://arxiv.org/abs/math/0508411

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