Enumerating Dihedral Hopf-Galois Structures Acting on Dihedral Extensions
| Autor: | Timothy Kohl |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Regular representation Block (permutation group theory) Group Theory (math.GR) Permutation group Dihedral angle Dihedral group Hopf algebra 01 natural sciences Separable space Combinatorics Field extension 16T05 (12F10 20B35) 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics - Group Theory Mathematics |
| DOI: | 10.48550/arxiv.1907.03844 |
| Popis: | The work of Greither and Pareigis details the enumeration of the Hopf-Galois structures (if any) on a given separable field extension. For an extension L / K which is classically Galois with G = G a l ( L / K ) the Hopf algebras in question are of the form ( L [ N ] ) G where N ≤ B = P e r m ( G ) is a regular subgroup that is normalized by the left regular representation λ ( G ) ≤ B . We consider the case where both G and N are isomorphic to a dihedral group D n for any n ≥ 3 . Using the normal block systems inherent to the left regular representation of each D n , (and every other regular permutation group isomorphic to D n ) we explicitly enumerate all possible such N which arise. |
| Databáze: | OpenAIRE |
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