Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerating Dihedral Hopf-Galois Structures Acting on Dihedral
  Extensions   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 $G=Gal(L/K)$ the Hopf algebras in
question are of the form $(L[N])^{G}$ where $N\leq B=Perm(G)$ is a regular
subgroup that is normalized by the left regular representation $\lambda(G)\leq
B$. We consider the case where both $G$ and $N$ are isomorphic to a dihedral
group $D_n$ for any $n\geq 3$. 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.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ