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arXiv · 2602.24070

Irreducible cuspidal modules of simple $n$-Lie algebras

Bakhrom Omirov·Gulkhayo Solijanova
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Abstract

This work devoted to the description of irreducible cuspidal modules over simple $n$-Lie algebras. Since the description of irreducible modules over $n$-Lie algebra $O^n$ are already well understood, we focus here on the irreducible cuspidal modules over $n$-Lie algebras of Wronskians and Jacobians. First, for a given $n$-Lie algebra $\mathcal{L}$, we analyze the possible Lie and Leibniz structures on $\wedge^{n-1} \mathcal{L}$ and $\otimes^{n-1} \mathcal{L}$ by thoroughly examining existing structures. Next, we classify the irreducible cuspidal modules over the $n$-Lie algebra of Wronskians defined on Laurent polynomials with degree-preserving derivations. Furthermore, we prove that these modules remain irreducible over the $n$-Lie algebra of Jacobians.

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Bakhrom Omirov, Gulkhayo Solijanova. 2026-02-27. Irreducible cuspidal modules of simple $n$-Lie algebras. https://arxiv.org/abs/2602.24070

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