Normal Hopf subalgebras, depth two and Galois extensions

Abstract

Let $S$ be the left $R$-bialgebroid of a depth two extension with centralizer $R$ as defined in math.QA/0108067. We show that the left endomorphism ring of depth two extension, not necessarily balanced, is a left $S$-Galois extension of $A^{\mathrm{op}}$. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We find a class of examples of the alternative Hopf algebroids in math.QA/0302325. We also characterize finite weak Hopf-Galois extensions using an alternate Galois canonical mapping with several corollaries: that these are depth two and that surjectivity of the Galois mapping implies its bijectivity.

superseded by my more recent preprints math.QA/0502188 and math.QA/0503194

References in corpus (2)

• Galois theory for weak Hopf algebras
• An action-free characterization of weak Hopf-Galois extensions

Cited by in corpus (3)

• Galois theory for bialgebroids, depth two and normal Hopf subalgebras
• A note on Galois theory for bialgebroids
• Finitary Galois extensions over noncommutative bases