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Journal of Lie Theory 29 (2019), No. 1, 191--220
Copyright Heldermann Verlag 2019

Metric Symplectic Lie Algebras

Mathias Fischer
Institut für Mathematik und Informatik, Walther-Rathenau-Strasse 47, 17487 Greifswald, Germany

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

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