Transposed Poisson Structures on Two Nambu 3-Lie Algebras

Key Points

Non-trivial derivations were observed in the Nambu 3-Lie algebras studied, alongside trivial Poisson structures.
Key results include the finitely generated nature of one Nambu 3-Lie algebra and its implications for structure functionality.
Analysis focused on the transposed Poisson structures and deduced the uniqueness of algebraic features present.
Findings highlight constraints on the types of Poisson structures possible, guiding future theoretical exploration.

Abstract

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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Transposed Poisson Structures on Two Nambu 3-Lie Algebras

Key Points

Abstract

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