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This article is cited in 2 scientific papers (total in 2 papers)
Locally Nilpotent Derivations of Free Algebra of Rank Two
Vesselin Drenskya, Leonid Makar-Limanovbc a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
b Department of Mathematics, Wayne State University Detroit, MI 48202, USA
c Department of Mathematics, The Weizmann Institute of Science, Rehovot 7610001, Israel
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.
Keywords:
free associative algebras, locally nilpotent derivations, algebras of constants.
Received: October 1, 2019; in final form November 13, 2019; Published online November 18, 2019
Citation:
Vesselin Drensky, Leonid Makar-Limanov, “Locally Nilpotent Derivations of Free Algebra of Rank Two”, SIGMA, 15 (2019), 091, 10 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1527 https://www.mathnet.ru/eng/sigma/v15/p91
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