On the transposed Poisson n-Lie algebras

2025/01/03 by Mashurov, Farukh
#17A30 #17A42 #17B63 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2501.01714

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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