Analysis reveals finitely generated Nambu 3-Lie algebras exhibit unique derivations, indicating limits on Poisson structures.
We describe the [Formula: see text]-derivations and transposed Poisson structures of the Nambu 3-Lie algebras [Formula: see text] and [Formula: see text]. Specifically, we first present that [Formula: see text] is finitely generated and graded. Then we find that [Formula: see text] has non-trivial [Formula: see text]-derivations and admits only trivial transposed Poisson structures. The 3-Lie algebra [Formula: see text] admits non-trivial transposed Poisson structures.
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Jiang et al. (2025) studied this question.
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