Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 419434 (2006) 

Four dimensional symplectic Lie algebrasGabriela OvandoCIEM  Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba 5000, Argentina; email: ovando@mate.uncor.eduAbstract: Invariant symplectic structures are determined in dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described either as solutions of the cotangent extension problem or as symplectic double extension of ${\mathbb R}^2$ by $\mathbb R$. For this all extensions of a two dimensional Lie algebra are determined. We also find Lie algebras which do not admit a symplectic form in higher dimensions. Keywords: symplectic structures, solvable Lie algebra, cotangent extension, symplectic double extensions Classification (MSC2000): 53D05; 22E25, 17B56 Full text of the article:
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