Galois extensions for coquasi-Hopf algebras

TL;DR

This paper extends the concepts of Galois and cleft extensions to coquasi-Hopf algebras, establishing new theoretical results including a Schneider type theorem and a generalization of Schauenburg's bialgebroid construction.

Contribution

It introduces the notions of Galois and cleft extensions for coquasi-Hopf algebras and proves key equivalences and a Schneider type theorem in this context.

Findings

Cleft extensions are characterized as Galois with the normal basis property.

A Schneider type theorem is established for coquasi-Hopf algebras with bijective antipode.

Schauenburg's bialgebroid construction is generalized for coquasi-Hopf algebras.

Abstract

The notions of Galois and cleft extensions are generalized for coquasi-Hopf algebras. It is shown that such an extension over a coquasi-Hopf algebra is cleft if and only if it is Galois and has the normal basis property. A Schneider type theorem is proven for coquasi-Hopf algebras with bijective antipode. As an application, we generalize Schauenburg's bialgebroid construction for coquasi-Hopf algebras.