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arXiv · 1609.03314

Symplectic Lie algebras with degenerate center

Mathias Fischer
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Abstract

Every symplectic Lie algebra with degenerate (including non-abelian nilpotent symplectic Lie algebras) has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the isomorphism classes of symplectic Lie algebras with degenerate center. We also give a classification scheme for nilpotent symplectic Lie algebras and compute a complete list of all 6-dimensional nilpotent symplectic Lie algebras, which removes some little inaccuracies in an older list.

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Mathias Fischer. 2016-09-12. Symplectic Lie algebras with degenerate center. https://arxiv.org/abs/1609.03314

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