The Structure of Hopf Algebras Acting on Dihedral Extensions
| Autor: | Koch, Alan, Kohl, Timothy, Truman, Paul J., Underwood, Robert |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages, 1 figure |
| Databáze: | arXiv |
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