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Research Article | Open Access

Non-associative and non-commutative Poisson structures on Filiform Lie algebras

Yuqiu Sheng1, Jixia Yuan2( )
School of Mathematical Sciences, Bohai University, Jinzhou 121013, China
School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China
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Abstract

In this paper, we study the non-associative and non-commutative Poisson structures on filiform Lie algebras L n and Q 2 m and then characterize the commutative and associative Poisson structures on L n and Q 2 m . Besides, we discuss the relationships between some non-associative algebras.

Keywords

Poisson algebrafiliform Lie algebracommutative algebraassociative algebra
CLC number: 17B05, 17B30, 17B56

References

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AIMS Mathematics
Volume 10 Issue 7,
July 2025
Pages 16460-16476
DOI: 10.3934/math.2025737

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Cite this article:
Sheng Y, Yuan J. Non-associative and non-commutative Poisson structures on Filiform Lie algebras. AIMS Mathematics, 2025, 10(7): 16460-16476. https://doi.org/10.3934/math.2025737

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Received: 15 April 2025
Revised: 06 July 2025
Accepted: 15 July 2025
Published: 15 July 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)