Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie algebras admitting symmetric, invariant and nondegenerate bilinear
  forms   We present structural properties of Lie algebras admitting symmetric,
invariant and nondegenerate bilinear forms. We show that these properties are
not satisfied by nilradicals of parabolic subalgebras of real split forms of
complex simple Lie algebras, neither by 2-step nilpotent Lie algebras
associated with graphs, with only few exceptions. These rare cases are,
essentially, abelian Lie algebras, the free 3-step nilpotent Lie algebra on
2-generators and the free 2-step nilpotent Lie algebra on 3-generators.

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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
11
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: adap-org
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
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The categories of this paper are: stat