We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called \emph{complex symplectic oxidation}, to construct certain complex symplectic Lie algebras of dimension $4n+4$ from those of dimension $4n$. We specialize this construction to the nilpotent case and apply complex symplectic oxidation to classify eight-dimensional nilpotent complex symplectic Lie algebras.

中文翻译：

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李代数上的复辛结构

我们研究了具有复杂辛结构的李代数，并开发了一种称为\emph{复杂辛氧化}的方法，以从维度 $4n$ 构造某些维度 $4n+4$ 的复杂辛李代数。我们将这种构造专门用于幂零情况，并应用复辛氧化对八维幂零复辛李代数进行分类。