Finite-dimensional subalgebras in polynomial Lie algebras of rank one

• Date: 2011
• Main Authors: Arzhantsev, I. V., Makedonskii, E. A., Petravchuk, A. P., Аржанцев, І.В., Македонський, Є. А., Петравчук, А. П.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2755
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $W_n(\mathbb{K})$ be the Lie algebra of derivations of the polynomial algebra $\mathbb{K}[X] := \mathbb{K}[x_1,... ,x_n]$ over an algebraically closed field $K$ of characteristic zero. A subalgebra $L \subseteq W_n(\mathbb{K})$ is called polynomial if it is a submodule of the $\mathbb{K}[X]$-mo...