The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions

Truman, Paul; Taylor, Stuart

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.

Citation

Truman, P., & Taylor, S. (2019). The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions

• Acceptance Date: Dec 11, 2018
• Publication Date: Mar 5, 2019
• Journal: New York Journal of Mathematics
• Print ISSN: 1076-9803
• Pages: 219-237
• Keywords: Hopf Galois structure, Hopf algebra, Galois extension, Wedderburn-Artin decomposition
• Publisher URL: http://nyjm.albany.edu/j/2019/25-13.html