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

Yuqiu Sheng; Jixia Yuan; Yuqiu Sheng; Jixia Yuan

doi:10.3934/math.2025737

AIMS Mathematics

2025, Volume 10, Issue 7: 16460-16476. doi: 10.3934/math.2025737

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Research article

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

Yuqiu Sheng ¹,
Jixia Yuan ^{2
,
,}

1.
School of Mathematical Sciences, Bohai University, Jinzhou 121013, China
2.
School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China

Received: 15 April 2025 Revised: 06 July 2025 Accepted: 15 July 2025 Published: 22 July 2025
MSC : 17B05, 17B30, 17B56

In this paper, we study the non-associative and non-commutative Poisson structures on filiform Lie algebras $ L_n $ and $ Q_{2m} $ and then characterize the commutative and associative Poisson structures on $ L_n $ and $ Q_{2m} $. Besides, we discuss the relationships between some non-associative algebras.
- Poisson algebra,
- filiform Lie algebra,
- commutative algebra,
- associative algebra
Citation: Yuqiu Sheng, Jixia Yuan. Non-associative and non-commutative Poisson structures on Filiform Lie algebras[J]. AIMS Mathematics, 2025, 10(7): 16460-16476. doi: 10.3934/math.2025737

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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_{2m} $ and then characterize the commutative and associative Poisson structures on $ L_n $ and $ Q_{2m} $. Besides, we discuss the relationships between some non-associative algebras.

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