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arXiv · 1405.7604

Hopf Galois Structures on Primitive Purely Inseparable Extensions

Alan Koch
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Abstract

Let $L/K$ be a primitive purely inseparable extension of fields of characteristic $p$, $\left[ L:K\right] >p.$ It is well known that $L/K$ is Hopf Galois for some Hopf algebra $H$, and it is suspected that $L/K$ is Hopf Galois for numerous choices of $H$. We construct a family of $K$-Hopf algebras $H$ for which $L$ is an $H$-Galois object. For some choices of $K$ we will exhibit an infinite number of such $H.$ We provide some explicit examples of the dual, Hopf Galois, structure on $L/K.$

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Alan Koch. 2014-05-29. Hopf Galois Structures on Primitive Purely Inseparable Extensions. https://arxiv.org/abs/1405.7604

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