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 STYLE
Koch, A., Kohl, T., Truman, P. J., & Underwood, R. (2019). The structure of hopf algebras acting on dihedral extensions. In Springer Proceedings in Mathematics and Statistics (Vol. 277, pp. 201–218). Springer New York LLC. https://doi.org/10.1007/978-3-030-11521-0_10
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