Kernels of derivations of polynomial rings and Casimir elements

  • L. P. Bedratyuk Хмельниц. нац. ун-т


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 $n ≤ 6$.
How to Cite
Bedratyuk, L. P. “Kernels of Derivations of Polynomial Rings and Casimir Elements”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 4, Apr. 2010, pp. 435–452,
Research articles