Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indefinite Einstein metrics on nice Lie groups   We introduce a systematic method to produce left-invariant, non-Ricci-flat
Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a
nice nilpotent Lie group, we give a simple algebraic characterization of
non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for
which the nice basis is orthogonal and a more general class associated to order
two permutations of the nice basis.
  We obtain classifications in dimension 8 and, under the assumption that the
root matrix is surjective, dimension 9; moreover, we prove that Einstein
nilpotent Lie groups of nonzero scalar curvature exist in every dimension $\geq
8$.

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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org