@article{Huang2024, 
author = {Junyuan Huang and Xueqing Chen and Zhiqi Chen and Ming Ding},
title = {On a conjecture on transposed Poisson    n-Lie algebras},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6709-6733},
keywords = {Lie algebra, Poisson algebra, transposed Poisson algebra, n-Lie algebra, transposed Poisson n-Lie algebra},
url = {https://www.sciopen.com/article/10.3934/math.2024327},
doi = {10.3934/math.2024327},
abstract = {The notion of a transposed Poisson    n-Lie algebra has been developed as a natural generalization of a transposed Poisson algebra. It was conjectured that a transposed Poisson    n-Lie algebra with a derivation gives rise to a transposed Poisson    (  n  +  1  )-Lie algebra. In this paper, we focus on transposed Poisson    n-Lie algebras. We have obtained a rich family of identities for these algebras. As an application of these formulas, we provide a construction of    (  n  +  1  )-Lie algebras from transposed Poisson    n-Lie algebras with derivations under a certain strong condition, and we prove the conjecture in these cases.}
}