Ancochea Bermúdez, José MaríaCampoamor Stursberg, Otto-Rudwig2023-06-202023-06-2020020092-787210.1081/AGB-120013316https://hdl.handle.net/20.500.14352/58399We introduce the product by generators of two nilpotent Lie algebras as a central extension of the direct sum and analyze symplectic structures on them. We show that, up to few exceptions, these products do not admit symplectic forms. Besides a general criterion, we indicate a procedure to construct symplectic forms in natural manner on quotient Lie algebras of certain products by generators.engjournal articlehttps//doi.org/10.1081/AGB-120013316http://0-www.tandfonline.com.cisne.sim.ucm.es/doi/pdf/10.1081/AGB-120013316restricted access512.554.3Álgebra1201 Álgebra