Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Presentation of affine Kac-Moody groups over rings   Tits has defined Steinberg groups and Kac-Moody groups for any root system
and any commutative ring R. We establish a Curtis-Tits-style presentation for
the Steinberg group St of any rank > 2 irreducible affine root system, for any
R. Namely, St is the direct limit of the Steinberg groups coming from the 1-
and 2-node subdiagrams of the Dynkin diagram. This leads to a completely
explicit presentation. Using this we show that St is finitely presented if the
rank is > 3 and R is finitely generated as a ring, or if the rank is 3 and R is
finitely generated as a module over a subring generated by finitely many units.
Similar results hold for the corresponding Kac-Moody groups when R is a
Dedekind domain of arithmetic type.

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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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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: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph