A Morita context and Galois extensions for Quasi-Hopf algebras

TL;DR

This paper explores the relationship between Morita contexts and Galois extensions in the setting of finite-dimensional quasi-Hopf algebras, extending classical Hopf algebra results to a more general framework.

Contribution

It establishes a Morita context linking smash products and invariants for quasi-Hopf algebras, and connects Galois extensions with this context, generalizing known Hopf algebra theory.

Findings

Established Morita context for quasi-Hopf algebra actions

Connected Galois extensions with Morita theory in this setting

Extended classical Hopf algebra results to quasi-Hopf algebras

Abstract

If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we prove that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A^{H}. We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.