Every almost abelian pseudo-Kähler Lie algebra is classified into seven families in all dimensions, and nilpotent almost abelian Lie algebras with a complex structure automatically admit pseudo-Kähler metrics.
Andrada, Hypersymplectic Lie algebras , J
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Almost abelian pseudo-K\"ahler Lie algebras
Every almost abelian pseudo-Kähler Lie algebra is classified into seven families in all dimensions, and nilpotent almost abelian Lie algebras with a complex structure automatically admit pseudo-Kähler metrics.