Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Nilpotent Derivations of Free Algebra of Rank Two   In commutative algebra, if $\delta$ is a locally nilpotent derivation of the
polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ of characteristic 0 and
$w$ is a nonzero element of the kernel of $\delta$, then $\Delta=w\delta$ is
also a locally nilpotent derivation with the same kernel as $\delta$. In this
paper we prove that the locally nilpotent derivation $\Delta$ of the free
associative algebra $K\langle X,Y\rangle$ is determined up to a multiplicative
constant by its kernel. We show also that the kernel of $\Delta$ is a free
associative algebra and give an explicit set of its free generators.

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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat