The Nowicki Conjecture for relatively free algebras

2018/08/15 by Centrone, Lucio, Findik, Sehmus
#13A50 #13N15 #16R10 #16S15 #16W25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1808.05299

Abstract

A linear locally nilpotent derivation of the polynomial algebra K[X_m] in m variables over a field K of characteristic 0 is called a Weitzenböck derivation. It is well known from the classical theorem of Weitzenböck that the algebra of constants K[X_m]^δ of a Weitzenböck derivation δ is finitely generated. Assume that δ acts on the polynomial algebra K[X_2d] in 2d variables as follows: δ(x_2i)=x_2i-1, δ(x_2i-1)=0, i=1,…,d. The Nowicki conjecture states that the algebra K[X_2d]^δ is generated by x₁,x₃.…,x_2d-1, and x_2i-1x_2j-x_2ix_2j-1, 1≤ i

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