Hopf Galois Structures on Primitive Purely Inseparable Extensions

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 $L/K.$

Prop. 3.1 strengthened, short section on modular extensions added

References in corpus (1)

• Scaffolds and integral Hopf Galois module structure on purely inseparable extensions

Cited by in corpus (1)

• Scaffolds and integral Hopf Galois module structure on purely inseparable extensions