On extension of classical Baer results to Poisson algebras

• Date: 2021
• Main Authors: Kurdachenko, L. A., Pypka, A. A., Subbotin, I. Ya.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: Poisson algebra; Lie algebra; subalgebra; ideal; center; hypercenter; zero divisor; finite dimension; nilpotency; 17B63; 17B65
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1758
• Journal Title: Algebra and Discrete Mathematics

In this paper we prove that if \(P\) is a Poisson algebra and the \(n\)-th hypercenter (center) of \(P\) has a finite codimension, then \(P\) includes a finite-dimensional ideal \(K\) such that \(P/K\) is nilpotent (abelian). As a corollary, we show that if the \(n\)th hypercenter of a Poisson algeb...