On the Galois theory of inseparable extensions

Hopf Galois structures on primitive purely inseparable extensions

Let L/K be a primitive purely inseparable extension of fields of characteristic p, [L : K] > p, p odd. 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 ...

Scaffolds and integral Hopf Galois module structure on purely inseparable extensions

Let p be prime. Let L/K be a finite, totally ramified, purely inseparable extension of local fields, [L : K] = p, n ≥ 2. It is known that L/K is Hopf Galois for numerous Hopf algebras H, each of which can act on the extension in numerous ways. For a certain collection of such H we construct “Hopf Galois scaffolds” which allow us to obtain a Hopf analogue to the Normal Basis Theorem for L/K. The...

Homotopy Theory of Hopf Galois Extensions

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.

Galois Theory for Arbitrary Field Extensions

Coalgebra-galois Extensions from the Extension Theory Point of View

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.