A note about the Nowicki conjecture on Weitzenb\"ock derivations

TL;DR

This paper connects the Nowicki conjecture on Weitzenb"ock derivations to classical invariant theory, simplifying the problem and potentially paving the way for new solutions.

Contribution

It reduces the Nowicki conjecture to a well-known problem in classical invariant theory, providing a new perspective on the conjecture.

Findings

Reduction of the Nowicki conjecture to classical invariant theory

Simplification of the problem structure

Potential for new approaches to the conjecture

Abstract

We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.