On extension of classical Baer results to Poisson algebras

On extension of classical Baer results to Poisson algebras

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...

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Bibliographic Details
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
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary: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.

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