Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallelepipeds, Nilpotent Groups, and Gowers Norms   In his proof of Szemeredi's Theorem, Gowers introduced certain norms that are
defined on a parallelepiped structure. A natural question is on which sets a
parallelepiped structure (and thus a Gowers norm) can be defined. We focus on
dimensions 2 and 3 and show when this possible, and describe a correspondence
between the parallelepiped structures nilpotent groups.

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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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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: gr-qc