Characteristically nilpotent Lie algebras and symplectic structures
arXiv:math/0409251
Abstract
We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space $H^2(\Lg,k)$ for certain Lie algebras $\Lg$. Among these Lie algebras are filiform CNLAs of dimension . It turns out that there are many examples of CNLAs which admit a symplectic structure. A generalization of a sympletic structure is an affine structure on a Lie algebra.