Kählerian oxidation and reduction of Lie algebras with Kähler structures

A Kähler structure on a real Lie algebra $\mathfrak{g}$ is a pair $(ω, J)$ of a 2-cocycle and a complex structure on $\mathfrak{g}$ which are compatible in the sense that $J$ is skew-symmetric with respect to $ω$. This paper investigates Kähler structures on Lie algebras, with a particular focus on