@article{Bedratyuk_2010, title={Kernels of derivations of polynomial rings and Casimir elements}, volume={62}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2878}, abstractNote={We propose an algorithm for the evaluation of elements of the kernel of an arbitrary derivation of a polynomial ring. The algorithm is based on an analog of the well-known Casimir element of a finite-dimensional Lie algebra. By using this algorithm, we compute the kernels of Weitzenböck derivation $d(x_i ) = x_{i−1},\; d(x_0) = 0,\;i = 0,…, n$, for the cases where $n ≤ 6$.}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Bedratyuk, L. P.}, year={2010}, month={Apr.}, pages={435–452} }