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首页> 外文期刊>Journal of algebra and its applications >THE CONJECTURE OF NOWICKI ON WEITZENBOCK DERIVATIONS OF POLYNOMIAL ALGEBRAS
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THE CONJECTURE OF NOWICKI ON WEITZENBOCK DERIVATIONS OF POLYNOMIAL ALGEBRAS

机译：多项式代数的Weitzenbock导数上的Nowicki的映象

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The Weitzenbock theorem states that if Delta is a linear locally nilpotent derivation of the polynomial algebra K[Z] = K[z(1), ... ,z(m)] over a field K of characteristic 0, then the algebra of constants of Delta is finitely generated. If m = 2n and the Jordan normal form of Delta consists of 2 x 2 Jordan cells only, we may assume that K[Z] = K[X, Y] and Delta(y(i)) = x(i), Delta(x(i)) = 0, i = 1, ... ,n. Nowicki conjectured that the algebra of constants K[X, Y](Delta) is generated by x(1), ... ,x(n) and x(i)y(j) - x(j)y(i), 1 <= i < j <= n. Recently this conjecture was confirmed in the Ph.D. thesis of Khoury with a very computational proof, and also by Derksen whose proof is based on classical results of invariant theory. In this paper we give an elementary proof of the conjecture of Nowicki which does not use any invariant theory. Then we. find a very simple system of de. ning relations of the algebra K[X, Y](Delta) which corresponds to the reduced Grobner basis of the related ideal with respect to a suitable admissible order, and present an explicit basis of K[X, Y](Delta) as a vector space.
机译：Weitzenbock定理指出，如果Delta是在特征0的场K上多项式代数K [Z] = K [z（1），...，z（m）]的线性局部幂等导数，则代数K Delta常数是有限生成的。如果m = 2n并且Delta的约旦范式仅由2 x 2个Jordan细胞组成，我们可以假定K [Z] = K [X，Y]和Delta（y（i））= x（i），Delta [x（i））= 0，i = 1，...，n。 Nowicki推测常数K [X，Y]Δ的代数是由x（1），...，x（n）和x（i）y（j）-x（j）y（i）生成的，1 <= i

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