Casimir elements and kernel of Weitzenbök derivation

Abstract

Let $k[X]:=k[x_0,x_1,...,x_n]$ be a polynomial algebra over a field $k$ of characteristic zero. We offer an algorithm for calculation of kernel of Weitzenbök derivation $d(x_i)=x_{i-1},...,$ $d(x_0)=0$, $i=\mathrm{1...}n$ that is based on an analogue of the well known Casimir elements of finite dimensional Lie algebras. By using this algorithm, the kernel is calculated in the case $n<7$.

14 pages