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Campoamor Stursberg, Otto-Rudwig 2023-06-20T10:35:58Z 2023-06-20T10:35:58Z 2003 0024-3795 10.1016/S0024-3795(03)00494-4 https://hdl.handle.net/20.500.14352/50719 https//doi.org/10.1016/S0024-3795(03)00494-4 http://www.sciencedirect.com/science/article/pii/S0024379503004944 We describe a class of nilpotent Lie algebras completely determined by their associated weight graph. These algebras also present two important structural properties: to admit naturally a symplectic form and to be isomorphic to the nilradical of a solvable complete rigid Lie algebra. These solvable algebras are proved to constitute a class of algebras where a symplectic form cannot exist. Finally we analyze the product by generators of the preceding algebras, and show that this operator preserves the property of being the maximal nilpotent ideal of a solvable rigid Lie algebra eng restricted access A graph theoretical determination of solvable complete rigid Lie algebras journal article