The Conjecture of Nowicki on Weitzenboeck derivations of polynomial algebras

Details The Conjecture of Nowicki on Weitzenboeck derivations of polynomial algebras The Conjecture of Nowicki on Weitzenboeck derivations of polynomial algebras

2008-04-18

arxiv.org/abs/0804.2933v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

The Weitzenboeck theorem states that the algebra of constants of a linear locally nilpotent derivation of the polynomial algebra K[Z]=K[z_1,...,z_m] in m variables over a field K of characteristic 0 is finitely generated. If m=2n and the Jordan normal form of the derivation consists of Jordan cells of size 2 only, we may assume that K[Z]=K[X,Y] and the derivation sends y_i to x_i and x_i to 0, i=1,...,n. Nowicki conjectured that the algebra of constants of this derivation is generated by x_1,...,x_n and x_iy_j-x_jy_i, i

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