On the transposed Poisson n-Lie algebras
Rings and Algebras
2025-04-16 v3
Abstract
We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity criterion for transposed Poisson algebras, proving that a transposed Poisson n-Lie algebra is simple if and only if its associated n-Lie algebra is simple. In addition, we study the strong condition for transposed Poisson n-Lie algebras, proving that it fails in the case of a free transposed Poisson 3-Lie algebra.
Keywords
Cite
@article{arxiv.2501.01714,
title = {On the transposed Poisson n-Lie algebras},
author = {Farukh Mashurov},
journal= {arXiv preprint arXiv:2501.01714},
year = {2025}
}