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arXiv · 1608.01490

On Lie algebras consisting of locally nilpotent derivations

A. P. Petravchuk·K. Ya. Sysak
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Abstract

Let $K$ be an algebraically closed field of characteristic zero and $A$ an integral $K$-domain. The Lie algebra $Der_{K}(A)$ of all $K$-derivations of $A$ contains the set $LND(A)$ of all locally nilpotent derivations. The structure of $LND(A)$ is of great interest, and the question about properties of Lie algebras contained in $LND(A)$ is still open. An answer to it in the finite dimensional case is given. It is proved that any finite dimensional (over $K$) subalgebra of $Der_{K}(A)$ consisting of locally nilpotent derivations is nilpotent. In the case $A=K[x, y],$ it is also proved that any subalgebra of $Der_{K}(A)$ consisting of locally nilpotent derivations is conjugated by an automorphism of $K[x, y]$ with a subalgebra of the triangular Lie algebra.

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A. P. Petravchuk, K. Ya. Sysak. 2016-08-04. On Lie algebras consisting of locally nilpotent derivations. https://arxiv.org/abs/1608.01490

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