Induced Hopf Galois structures

TL;DR

This paper explores how to construct and characterize Hopf Galois structures on finite Galois extensions by inducing them from structures on intermediate subextensions, providing a new perspective on their formation.

Contribution

It introduces a method to induce Hopf Galois structures on Galois extensions from structures on intermediate fields, expanding understanding of their construction.

Findings

Characterization of induced Hopf Galois structures

Conditions for normal complements in Galois groups

Framework for constructing Hopf Galois structures

Abstract

For a finite Galois extension K/k and an intermediate field F such that Gal(K/F) has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois structures on K/F and F/k.