
Journal of Lie Theory 29 (2019), No. 1, 191220 Copyright Heldermann Verlag 2019 Metric Symplectic Lie Algebras Mathias Fischer Institut für Mathematik und Informatik, WaltherRathenauStrasse 47, 17487 Greifswald, Germany mathias.fischer@unigreifswald.de It is shown that any metric symplectic Lie algebra has the structure of a quadratic extension. A standard model for such extensions is proposed, and the equivalence classes at the level of the quadratic cohomology sets is given. Further, a classification scheme for metric symplectic Lie algebras is provided, as well as an explicit list of isomorphism classes for some special types. Keywords: Metric Lie algebra, symplectic Lie algebra, symmetric space. MSC: 53C35, 53D20, 17B30 [ Fulltextpdf (210 KB)] for subscribers only. 