The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in for polynomial algebras and in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson algebra.
Lie algebras, Poisson algebras, the Nowicki conjecture
CENTRONE, LUCIO; DUSHIMIRIMANA, ANDRE; and FINDIK, ŞEHMUS
"On Nowicki's conjecture: a survey and a new result,"
Turkish Journal of Mathematics: Vol. 46:
5, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss5/7