RESEARCH ARTICLE

On extension of classical Baer results to Poisson algebras

L. A. Kurdachenko^a, A. A. Pypka^a, I. Ya. Subbotin<sup>b

a</sup> Oles Honchar Dnipro National University, Gagarin ave., 72, Dnipro, 49010, Ukraine
^b National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, USA

Аннотация: 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 algebra $P$ (over some specific field) has a finite codimension and $P$ does not contain zero divisors, then $P$ is an abelian algebra.

Ключевые слова: Poisson algebra, Lie algebra, subalgebra, ideal, center, hypercenter, zero divisor, finite dimension, nilpotency.

MSC: 17B63, 17B65

Поступила в редакцию: 15.01.2021

Язык публикации: английский

DOI: 10.12958/adm1758