Kernels of derivations of polynomial rings and Casimir elements - Bedratyuk, L. P. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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.