On Nowicki's conjecture: a survey and a new result

TL;DR

This paper surveys existing tools and literature on Nowicki's conjecture in associative algebras and presents a new result confirming the conjecture for free metabelian Poisson algebras.

Contribution

It provides an extensive overview of methods related to Nowicki's conjecture and introduces a novel proof for the conjecture within free metabelian Poisson algebras.

Findings

Established new proof for Nowicki's conjecture in free metabelian Poisson algebras

Compiled comprehensive tools and bibliography on Nowicki's conjecture in associative settings

Extended understanding of the conjecture's validity in specific algebraic structures

Abstract

The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson algebra.