Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric Systems and their Applications to Root Systems Extended by
  Abelian Groups   We investigate the class of root systems R obtained by extending an
irreducible root system by a torsion-free group G. In this context there is a
Weyl group W and a group U with the presentation by conjugation. We show under
additional hypotheses that the kernel of the natural homomorphism from U to W
is isomorphic to the kernel of the homomorphism from the abelianization of U to
that of W. For this we introduce the concept of a symmetric system, a discrete
version of the concept of a symmetric space. Mathematics Subject Classification
2000: 20F55, 17B65, 17B67, 22E65, 22E40. Key Words and Phrases: Weyl group,
root system, presentation by conjugation, extended affine Weyl group (EAWeG),
extended affine root system (EARS), irreducible root system extended by an
abelian group.

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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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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: ao-sci