Deformations of graded Lie algebras and symplectic structures

We study symplectic structures on filiform Lie algebras – nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following form: $$[e_i,e_j]=(j-i)e_{i+j}+\sum _{l=1}{c}_{ij}^l{e}_{i+j+l},i+j\le n\mathrm{.}$$ In even dimensions the subspace of symplectic Lie algebras has the codimension one.