 

Lindsay N. Childs
On the Galois correspondence for Hopf Galois structures view print


Published: 
January 2, 2017

Keywords: 
Hopf Galois extension, finite commutative nilpotent ring, Fundamental Theorem of Galois Theory 
Subject: 
Primary 12F10, secondary 13M05 


Abstract
We study the question of the surjectivity of the Galois correspondence from subHopf algebras to subfields given by the Fundamental Theorem of Galois Theory for abelian Hopf Galois structures on a Galois extension of fields with Galois group Γ, a finite abelian pgroup. Applying the connection between regular subgroups of the holomorph of a finite abelian pgroup (G, +) and associative, commutative nilpotent algebra structures A on (G, +), we show that if A gives rise to a HHopf Galois structure on L/K, then the KsubHopf algebras of H correspond to the ideals of A. Among the applications, we show that if G and Γ are both elementary abelian pgroups, then the only Hopf Galois structure on L/K of type G for which the Galois correspondence is surjective is the classical Galois structure.


Author information
Department of Mathematics and Statistics, University at Albany, Albany, NY 12222
lchilds@albany.edu

