Depth Two and the Galois Coring

2004/08/11 by Lars Kadison, Kadison, Lars
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.QA #math.RA #msc:16A24

paper · pdf · doi:10.48550/arxiv.math/0408155

9 pages

arxiv created 2004/08/11 · arxiv updated 2009/12/01

Abstract

We study the cyclic module _SR for a ring extension A ‖ B with centralizer R and bimodule endomorphism ring S = End _BA_B. We show that if A ‖ B is an H-separable Hopf subalgebra, then B is a normal Hopf subalgebra of A. We observe from math.RA/0107064 and math.RA/0108067 depth two in the role of noncommutative normality (as in field theory) in a depth two separable Frobenius characterization of irreducible semisimple-Hopf-Galois extensions. We prove that a depth two extension has a Galois A-coring structure on A ø_R T where T is the right R-bialgebroid dual to S.

Related

• Normal Hopf subalgebras, depth two and Galois extensions
• Depth two, normality and a trace ideal condition for Frobenius extensions
• Hopf algebroids and Galois extensions
• Dual Bialgebroids for Depth Two Ring Extensions
• Semisimple Hopf algebras and their depth two Hopf subalgebras