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Casimir elements and kernel of Weitzenb\"ok derivation

L. Bedratyuk
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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 Weitzenb\"ok derivation ${d(x_i)=x_{i-1}}, ...,$ ${d(x_0)=0}$, ${i=1... n}$ 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 $n <7$.

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BibTeXRIS

L. Bedratyuk. 2005-12-22. Casimir elements and kernel of Weitzenb\"ok derivation. https://arxiv.org/abs/math/0512520

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