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arXiv · 1708.09822

The Structure of Hopf Algebras Acting on Dihedral Extensions

Alan Koch·Timothy Kohl·Paul J. Truman·Robert Underwood
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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 $D_p$, $p\ge 3$ 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.

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Alan Koch, Timothy Kohl, Paul J. Truman, Robert Underwood. 2019-03-22. The Structure of Hopf Algebras Acting on Dihedral Extensions. https://arxiv.org/abs/1708.09822

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