Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete Reducibility in Euclidean Twin Buildings   Completely reducible subcomplexes of spherical buildings was defined by J.P.
Serre and are used in studying subgroups of reductive algebraic groups. We
begin the study of completely reducible subcomplexes of twin buildings and how
they may be used to study subgroups of algebraic groups over a ring of Laurent
polynomials and Kac-Moody groups by looking at the Euclidean twin building
case.

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The categories of this paper are: quant-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: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con