Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical deformations of three-dimensional Lie algebras in Bianchi
  classification over the harmonic oscillator   Operadic Lax representations for the harmonic oscillator are used to
construct the dynamical deformations of three-dimensional (3D) real Lie
algebras in the Bianchi classification. It is shown that the energy
conservation of the harmonic oscillator is related to the Jacobi identities of
the dynamically deformed algebras. Based on this observation, it is proved that
the dynamical deformations of 3D real Lie algebras in the Bianchi
classification over the harmonic oscillator are Lie algebras.

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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex