Another proof of the Nowicki conjecture

2019/02/23 by Drensky, Vesselin
#13A50 #13N15 #15A72 #20G05 #22E46 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1902.08758

Abstract

Let K[X_d,Y_d]=K[x₁,…,x_d,y₁,…,y_d] be the polynomial algebra in 2d variables over a field K of characteristic 0 and let δ be the derivation of K[X_d,Y_d] defined by δ(y_i)=x_i, δ(x_i)=0, i=1,…,d. In 1994 Nowicki conjectured that the algebra K[X_d,Y_d]^δ of constants of δ is generated by X_d and x_iy_j-y_ix_j for all 1≤ i

Related

• The Nowicki Conjecture for relatively free algebras
• The Conjecture of Nowicki on Weitzenboeck derivations of polynomial algebras
• The Nowicki Conjecture for free metabelian Lie algebras
• Generalized Nowicki conjecture
• On the Nowicki Conjecture for the free Lie algebra of rank 2