An action-free characterization of weak Hopf-Galois extensions

2004/09/29 by Lars Kadison, Kadison, Lars
Mathematics · #13B05 #16W30 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA #msc:13B05 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0409589

5 pages, clarification of main theorem with thanks to the referee of Algebra Montpellier Announcements

openalex publication_date 2004/09/29 · arxiv created 2004/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define comodule algebras and Galois extensions for actions of bialgebroids. Using just module conditions we characterize the Frobenius extensions that are Galois as depth two and right balanced extensions. As a corollary, we obtain characterizations of certain weak and ordinary Hopf-Galois extensions without reference to action in the hypothesis.

Related

• Galois theory for bialgebroids, depth two and normal Hopf subalgebras
• A note on Galois theory for bialgebroids
• Galois actions by finite quantum groupoids
• Dual Bialgebroids for Depth Two Ring Extensions
• Hopf algebra actions on strongly separable extensions of depth two