On the transposed Poisson n-Lie algebras

Farukh Mashurov

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arXiv · 2501.01714

On the transposed Poisson n-Lie algebras

Farukh Mashurov

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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.

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Farukh Mashurov. 2025-01-03. On the transposed Poisson n-Lie algebras. https://arxiv.org/abs/2501.01714

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