Galois theory for weak Hopf algebras

Abstract

We develop Hopf-Galois theory for weak Hopf algebras, and recover analogs of classical results for Hopf algebras. Our methods are based on the recently introduced Galois theory for corings. We focus on the situatation where the weak Hopf algebra is a groupoid algebra or its dual. We obtain weak versions of strongly graded rings, and classical Galois extensions.

24 pages

Cited by in corpus (12)

• Partial groupoid actions: globalization, Morita theory and Galois theory
• (Co)cyclic (co)homology of bialgebroids: An approach via (co)monads
• The Ideal Intersection Property for Groupoid Graded Rings
• On the 2-categories of weak distributive laws
• Duality for groupoid (co)actions
• An action-free characterization of weak Hopf-Galois extensions
• Normal Hopf subalgebras, depth two and Galois extensions
• Irreducible actions and compressible modules
• Kaplansky's Construction Type and Classification of Weak bialgebras and Weak Hopf algebras
• Some interactions between Hopf Galois extensions and noncommutative rings
• The structure of weak coalgebra-Galois extensions
• Finitary Galois extensions over noncommutative bases