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arXiv · 1909.13262

Locally Nilpotent Derivations of Free Algebra of Rank Two

Vesselin Drensky·Leonid Makar-Limanov
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Abstract

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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Vesselin Drensky, Leonid Makar-Limanov. 2019-09-29. Locally Nilpotent Derivations of Free Algebra of Rank Two. https://doi.org/10.3842/sigma.2019.091

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