Transposed poisson structures on two Nambu 3-Lie algebras

In this paper, 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 nontrivial [Formula: see text]-derivations and admits only trivial transposed Poisson structures. The 3-Lie algebra [Formula: see text] admits nontrivial transposed Poisson structures.