The Structure of Hopf Algebras Acting on Dihedral Extensions

Koch, Alan; Kohl, Timothy; Truman, Paul J.; Underwood, Robert

Abstract

We discuss isomorphism questions concerning the Hopf algebras that yield Hopf–Galois structures for a fixed separable field extension L/K. We study in detail the case where L/K is Galois with dihedral group Dp, p=3 prime and give explicit descriptions of the Hopf algebras which act on L/K. We also determine when two such Hopf algebras are isomorphic, either as Hopf algebras or as algebras. For the case p=3 and a chosen L/K, we give the Wedderburn–Artin decompositions of the Hopf algebras.

Citation

Koch, A., Kohl, T., Truman, P. J., & Underwood, R. (2019). The Structure of Hopf Algebras Acting on Dihedral Extensions. In Advances in Algebra. SRAC 2017 (201-218)

• Acceptance Date: Apr 20, 2017
• Publication Date: Feb 27, 2019
• Pages: 201-218
• Book Title: Advances in Algebra. SRAC 2017
• ISBN: 978-3-030-11520-3