Mathematics – Algebraic Geometry
Scientific paper
2005-12-22
Ukrainian Math. Journal, 62, No. 4, pp. 435-452, (2010)
Mathematics
Algebraic Geometry
14 pages
Scientific paper
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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