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Eight-dimensional non completely reducible symplectic Lie algebras
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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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