Campoamor Stursberg, Otto-Rudwig2023-06-202023-06-2020030024-379510.1016/S0024-3795(03)00494-4https://hdl.handle.net/20.500.14352/50719We 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 algebraengjournal articlehttps//doi.org/10.1016/S0024-3795(03)00494-4http://www.sciencedirect.com/science/article/pii/S0024379503004944restricted access512Lie algebraSymplecticGraphCompleteWeightÁlgebra1201 Álgebra