Item

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.