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December 2020 Another Proof of the Nowicki Conjecture
Vesselin DRENSKY
Tokyo J. Math. 43(2): 537-542 (December 2020). DOI: 10.3836/tjm/1502179320

Abstract

Let $K[X_d,Y_d]=K[x_1,\ldots,x_d,y_1,\ldots,y_d]$ be the polynomial algebra in $2d$ variables over a field $K$ of characteristic 0 and let $\delta$ be the derivation of $K[X_d,Y_d]$ defined by $\delta(y_i)=x_i$, $\delta(x_i)=0$, $i=1,\ldots,d$. In 1994 Nowicki conjectured that the algebra $K[X_d,Y_d]^{\delta}$ of constants of $\delta$ is generated by $X_d$ and $x_iy_j-y_ix_j$ for all $1\leq i<j\leq d$. The affirmative answer was given by several authors using different ideas. In the present paper we give another proof of the conjecture based on representation theory of the general linear group $GL_2(K)$.

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Vesselin DRENSKY. "Another Proof of the Nowicki Conjecture." Tokyo J. Math. 43 (2) 537 - 542, December 2020. https://doi.org/10.3836/tjm/1502179320

Information

Published: December 2020
First available in Project Euclid: 18 June 2020

MathSciNet: MR4185848
Digital Object Identifier: 10.3836/tjm/1502179320

Subjects:
Primary: 13N15
Secondary: 13A50, 15A72, 20G05, 22E46

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 2 • December 2020
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