Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic free resolutions and root systems   In this paper I give an explicit construction of the generic ring R_{gen} for
finite free resolutions of length 3. The corresponding problem for resolutions
of length 2 was solved in 1970'ies by Hochster and Huneke. The key role is
played by the defect Lie algebra introduced in my old work on the subject. The
defect Lie algebra turns out to be a parabolic Lie algebra in a Kac-Moody Lie
algebra associated to the graph T_{p,q,r} corresponding to the format of the
resolution. The ring R_{gen} is Noetherian if and only if the graph T_{p.q.r}
is a Dynkin graph.

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The categories of this paper are: hep-th
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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: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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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: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org