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- W4289693766 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 Weitzenbock derivation. It is well known from the classical theorem of Weitzenbock that the algebra of constants $K[X_{m}]^{delta}$ of a Weitzenbock derivation $delta$ is finitely generated. Assume that $delta$ acts on the polynomial algebra $K[X_{2d}]$ in $2d$ variables as follows: $delta(x_{2i})=x_{2i-1}$, $delta(x_{2i-1})=0$, $i=1,ldots,d$. The Nowicki conjecture states that the algebra $K[X_{2d}]^{delta}$ is generated by $x_1,x_3.ldots,x_{2d-1}$, and $x_{2i-1}x_{2j}-x_{2i}x_{2j-1}$, $1leq i<jleq d$. The conjecture was proved by several authors based on different techniques. We apply the same idea to two relatively free algebras of rank $2d$. We give the infinite set of generators of the algebra of constants in the the free metabelian associative algebras $F_{2d}(mathfrak A)$, and finite set of generators in the free algebra $F_{2d}(mathcal G)$ in the variety determined by the identities of the infinite dimensional Grassmann algebra." @default.
- W4289693766 created "2022-08-04" @default.
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- W4289693766 date "2018-08-15" @default.
- W4289693766 modified "2023-09-26" @default.
- W4289693766 title "The Nowicki Conjecture for relatively free algebras" @default.
- W4289693766 doi "https://doi.org/10.48550/arxiv.1808.05299" @default.
- W4289693766 hasPublicationYear "2018" @default.
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