Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nilpotent Lie algebras of derivations of fraction fields   Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative
associative $ K$-algebra which is an integral domain. Denote by $R$ the
fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of
$\mathbb K$-derivations of $R$ obtained from $Der_{\mathbb K}A$ via
multiplication by elements of $R.$ If $L\subseteq W(A)$ is a subalgebra of
$W(A)$ denote by $rk_{R}L$ the dimension of the vector space $RL$ over the
field $R$ and by $F=R^{L}$ the field of constants of $L$ in $R.$ Let $L$ be a
nilpotent subalgebra $L\subseteq W(A)$ with $rk_{R}L\leq 3$. It is proven that
the Lie algebra $FL$ (as a Lie algebra over the field $F$) is isomorphic to a
finite dimensional subalgebra of the triangular Lie subalgebra $u_{3}(F)$ of
the Lie algebra $Der F[x_{1}, x_{2}, x_{3}], $ where $u_{3}(F)=\{f(x_{2},
x_{3})\frac{\partial}{\partial x_{1}}+g(x_{3})\frac{\partial}{\partial
x_{2}}+c\frac{\partial}{\partial x_{3}}\}$ with $f\in F[x_{2}, x_{3}], g\in
F[x_3]$, $c\in F.$ In particular, a characterization of nilpotent Lie algebras
of vector fields with polynomial coefficients in three variables is obtained.

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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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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: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph