Symplectic Lie algebras with degenerate center

TL;DR

This paper classifies symplectic Lie algebras with degenerate centers, providing a standard model, equivalence classes, and a complete list of 6-dimensional nilpotent cases, refining previous classifications.

Contribution

It introduces a classification scheme for symplectic Lie algebras with degenerate centers, including nilpotent cases, and corrects earlier incomplete lists.

Findings

Standard model for symplectic Lie algebras with degenerate center

Classification scheme for nilpotent symplectic Lie algebras

Complete list of 6-dimensional nilpotent symplectic Lie algebras

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.