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arXiv · 2506.13699

Eight-dimensional non completely reducible symplectic Lie algebras

T. Aït Aissa·S. El Bourkadi·M. W. Mansouri·SM. Sbai
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Abstract

A non completely reducible symplectic Lie algebra is a symplectic Lie algebra which cannot be symplectically reduced to the trivial symplectic Lie algebra. Our aim is to provide a complete classification, up to symplectomorphism of non completely reducible symplectic Lie algebras in dimensions $n \leq 8$ and, furthermore, to provide a complete description of symplectic Lie algebras admitting one-dimensional isotropic ideals.

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T. Aït Aissa, S. El Bourkadi, M. W. Mansouri, SM. Sbai. 2025-06-16. Eight-dimensional non completely reducible symplectic Lie algebras. https://arxiv.org/abs/2506.13699

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