Truman, PJ, Koch, A, Kohl, T and Underwood, R (2019) The Structure of Hopf Algebras Acting on Dihedral Extensions. In: Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, 277 . Springer, pp. 201-218. ISBN 978-3-030-11520-3

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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.

Item Type: Book Section
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 09 Jul 2018 09:15
Last Modified: 27 Feb 2021 01:30

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