Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weyl group of type $A_1$ root systems extended by an abelian group   We investigate the class of root systems $R$ obtained by extending an
$A_1$-type irreducible root system by a free abelian group $G$. In this context
there is a Weyl group $W$ and a group $U$ with the presentation by conjugation.
Both groups are reflection groups with respect to a discrete symmetric space
$T$ associated to $R$. We show that the natural homomorphism $U\to W$ is an
isomorphism if and only if an associated subset $T^{ab}\setminus\{0\}$ of
$G_2=G/2G$ is 2-independent, i.e. its image under the map $G_2\to G_2\otimes
G_2, g\mapsto g\otimes g$ is linearly independent over the Galois field $F_2$.

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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an