Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three Dimensional Lorentz homogeneous spaces and the Petrov
  classification   In this note, we verify the classification of local geometries given by A.Z.
Petrov. First, we determine criteria for identifying a given 3D Lorentz
homogeneous space in Petrov's classification. Then, we identify all
inequivalent 1D subalgebras of all real 4D Lie algebras and determine which of
these give rise to a homogeneous space admitting an invariant Lorentz metric.

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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg