Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 419-434 (2006)

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Four dimensional symplectic Lie algebras

Gabriela Ovando

CIEM - Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba 5000, Argentina; e-mail:

Abstract: 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

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Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

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