Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of Divergence-Free Lie Algebras   One of the four well-known series of simple Lie algebras of Cartan type is
the series of Lie algebras of Special type, which are divergence-free Lie
algebras associated with polynomial algebras and the operators of taking
partial derivatives, connected with volume-preserving diffeomorphisms. In this
paper, we determine the structure space of the divergence-free Lie algebras
associated with pairs of a commutative associative algebra with an identity
element and its finite-dimensional commutative locally-finite derivation
subalgebra such that the commutative associative algebra is derivation-simple
with respect to the derivation subalgebra.

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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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: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat