Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classification of exceptional components in group algebras over
  abelian number fields   When considering the unit group of $\mathcal{O}_F G$ ($\mathcal{O}_F$ the
ring of integers of an abelian number field $F$ and a finite group $G$) certain
components in the Wedderburn decomposition of $FG$ cause problems for known
generic constructions of units; these components are called exceptional.
Exceptional components are divided into two types: type 1 are division rings,
type 2 are $2 \times 2$-matrix rings. For exceptional components of type 1 we
provide infinite classes of division rings by describing the seven cases of
minimal groups (w.r.t. quotients) having those division rings in their
Wedderburn decomposition over $F$. We also classify the exceptional components
of type 2 appearing in group algebras of a finite group over number fields $F$
by describing all 58 finite groups $G$ having a faithful exceptional Wedderburn
component of this type in $FG$.

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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th