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arXiv · 2011.07578

Minimal Hopf-Galois Structures on Separable Field Extensions

Tony Ezome·Cornelius Greither
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Abstract

In Hopf-Galois theory, every $H$-Hopf-Galois structure on a field extension $K/k$ gives rise to an injective map $\mathcal{F}$ from the set of $k$-sub-Hopf algebras of $H$ into the intermediate fields of $K/k$. Recent papers on the failure of the surjectivity of $\mathcal{F}$ reveal that there exist many Hopf-Galois structures for which there are many more subfields than sub-Hopf algebras. This paper surveys and illustrates group-theoretical methods to determine $H$-Hopf-Galois structures on finite separable extensions in the extreme situation when $H$ has only two sub-Hopf algebras.

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Tony Ezome, Cornelius Greither. 2020-11-15. Minimal Hopf-Galois Structures on Separable Field Extensions. https://arxiv.org/abs/2011.07578

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