Thursday 22 Mar 2018: Isomorphism problems for Hopf-Galois structures on separable field extensions
Paul Truman - Keele University
Let L/K be a finite extension of fields. A Hopf-Galois structure on L/K consists of a Hopf algebra H together with a certain type of action of H on L. In the case that L/K is an extension of local or global fields, Hopf-Galois structures can provide a variety of contexts in which we can ask module theoretic questions about the extension and its fractional ideals. In the case that L/K is separable, a theorem of Greither and Pareigis classifies the Hopf-Galois structures admitted by L/K and shows that the Hopf algebras that occur are all twisted forms of group algebras. We establish criteria for two such Hopf algebras to be isomorphic as Hopf algebras, and study the more delicate question of when they are isomorphic as K-algebras.