Akademik Veri Yönetim Sistemi
Communications in Mathematics, cilt.33, sa.3, ss.1-18, 2025 (Scopus)
Let K[Xn ] = K[x1,…,xn] be the polynomial algebra in n variables over a field K of characteristic zero. A locally nilpotent linear derivation δ of K[Xn ] is called Weitzenböck due to his well known result from 1932 stating that the algebra of constants of δ defined by ker(δ) = K[Xn ]δ is finitely generated. The explicit form of a generating set of K[Xn,Yn]δ was conjectured by Nowicki in 1994 in the case δ was such that δ(yi ) = xi, δ(xi ) = 0, i = 1,…,n. Nowicki’s conjecture turned out to be true and, recently, has been applied to several relatively free associative algebras. In this paper, we consider the free Lie algebra L(x,y) of rank 2 generated by x and y over K and we assume the Weitzenböck derivation δ sending y to x, and x to zero. We introduce the idea of pseudodeterminants and we present a characterization of Hall monomials that are constants showing they are not so far from being pseudodeterminants. We also give a complete list of generators of the constants of degree less than 7 which are, of course, pseudodeterminants.