Depth Two and the Galois Coring

Details Depth Two and the Galois Coring Depth Two and the Galois Coring

2004-08-11

arxiv.org/abs/math/0408155v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

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 $A \o_R T$ where $T$ is the right $R$-bialgebroid dual to $S$.

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