Locally Nilpotent Derivations of Free Algebra of Rank Two

Symmetry Integrability and Geometry-Methods and Applications

article

Vesselin Drensky¹  Leonid Makar-Limanov² 

[1] Institute of Mathematics and Informatics, Bulgarian Academy of Sciences;Department of Mathematics, Wayne State University Detroit

关键词: free associative algebras;    locally nilpotent derivations;    algebras of constant;   

DOI  :  10.3842/SIGMA.2019.091

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown