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arXiv · 2606.03449

A complete description of solvable symplectic Lie algebras

Abdelhak Abouqateb·Saïd Benayadi·Othmane Dani
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Abstract

In this paper, we present a complete characterization of solvable symplectic Lie algebras via a symplectic double extension process. We demonstrate that any such algebra is either symplectically irreducible or can be constructed through a finite sequence of symplectic double extensions by a line or a plane, starting from symplectically irreducible Lie algebras. Furthermore, we show that if a symplectic Lie algebra has a nondegenerate derived ideal, then it is necessarily unimodular and, in particular, solvable. Finally, we present a novel algebraic proof of a classical structural theorem on symplectically irreducible symplectic Lie algebras and classify all Lie algebras of dimension up to $6$ that admit such structures.

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Abdelhak Abouqateb, Saïd Benayadi, Othmane Dani. 2026-06-02. A complete description of solvable symplectic Lie algebras. https://arxiv.org/abs/2606.03449

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