Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-metric 2-step nilpotent Lie algebras   The metric approach to studying 2-step nilpotent Lie algebras by making use
of non-degenerate scalar products is realised. We show that any 2-step
nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is
a 2-step nilpotent Lie algebra endowed with some standard non-degenerate scalar
product compatible with Lie brackets. This choice of the standard pseudo-metric
form allows to study the isomorphism properties. If the elements of the centre
of the standard pseudo-metric form constitute a Lie triple system of the
pseudo-orthogonal Lie algebra, then the original 2-step nilpotent Lie algebra
admits integer structure constants. Among particular applications we prove that
pseudo $H$-type algebras have bases with rational structural constants, which
implies that the corresponding pseudo $H$-type groups admit lattices.

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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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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: nucl-th
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The categories of this paper are: gr-qc