Deformations of graded Lie algebras and symplectic structures
Abstract
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: [ei,ej]=(j-i)ei+j+Σl=1cijl ei+j+l, i+j n. In even dimensions the subspace of symplectic Lie algebras has the codimension one.
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