Kernels of derivations of polynomial rings and Casimir elements
Abstract
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 $n ≤ 6$.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 4, pp 495-517.
Citation Example: Bedratyuk L. P. Kernels of derivations of polynomial rings and Casimir elements // Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 435–452.
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