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Normal Hopf subalgebras, depth two and Galois extensions

Lars Kadison
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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 $A^{\rm op}$. 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.

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Lars Kadison. 2005-04-06. Normal Hopf subalgebras, depth two and Galois extensions. https://arxiv.org/abs/math/0411129

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