@article { ,
title = {The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions},
abstract = {Let L/F be a Galois extension of fields with Galois group isomorphic to the quaternion group of order 8. We describe all of the Hopf-Galois structures admitted by L/F, and determine which of the Hopf algebras that appear are isomorphic as Hopf algebras. In the case that F has characteristic not equal to 2 we also determine which of these Hopf algebras are isomorphic as F-algebras and explicitly compute their Wedderburn-Artin decompositions.},
issn = {1076-9803},
journal = {New York Journal of Mathematics},
note = {This is the accepted author manuscript (AAM). The final published version (version of record) is available online via the website of the New York Journal of Mathematics at http://nyjm.albany.edu/nyjm.html - please refer to any applicable terms of use of the publisher.},
pages = {219-237},
publicationstatus = {Published},
keyword = {QA Mathematics, Hopf Galois structure, Hopf algebra, Galois extension, Wedderburn-Artin decomposition},
year = {2019},
author = {Truman, Paul and Taylor, Stuart}
}