Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bianchi spaces and their 3-dimensional isometries as S-expansions of
  2-dimensional isometries   In this paper we show that some 3-dimensional isometry algebras, specifically
those of type I, II, III and V (according Bianchi's classification), can be
obtained as expansions of the isometries in 2 dimensions. It is shown that in
general more than one semigroup will lead to the same result. It is impossible
to obtain the algebras of type IV, VI-IX as an expansion from the isometry
algebras in 2 dimensions. This means that the first set of algebras has
properties that can be obtained from isometries in 2 dimensions while the
second set has properties that are in some sense intrinsic in 3 dimensions. All
the results are checked with computer programs. This procedure can be
generalized to higher dimensions, which could be useful for diverse physical
applications.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int