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Symmetric polynomials in the free metabelian Poisson algebras

Andre Dushimirimana

Department of Mathematics, Çukurova University, Adana, Turkey

E-mail Address: duandosh@yahoo.fr

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Şehmus Fındık

Department of Mathematics, Çukurova University, Adana, Turkey

E-mail Address: sfindik@cu.edu.tr

Corresponding author.

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, and

Nazar Şahi̇n Öğüşlü

Department of Mathematics, Çukurova University, Adana, Turkey

E-mail Address: noguslu@cu.edu.tr

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https://doi.org/10.1142/S0219498823500494Cited by:1 (Source: Crossref)

Abstract

Let K be a field of characteristic zero and $X_{n} = {x_{1}, \dots, x_{n}}$ be a finite set of variables. Consider the free metabelian Poisson algebra $P_{n}$ of rank n generated by $X_{n}$ over K. An element in $P_{n}$ is called symmetric if it is preserved under any change of variables, i.e. under the action of each permutation in $S_{n}$ . In this study, we determine the algebra $P_{n}^{S_{n}}$ of symmetric polynomials of $P_{n}$ .

Communicated by Shun-Jen Cheng

Keywords:

AMSC: 17B01, 17B30, 16S15

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