We classify four-dimensional para-Kähler Lie algebras and study their geometry showing that they are symmetric or simply harmonic special recurrent, in the semi-symmetric case. The non-semi-symmetric case allows essentially two distinct geometries in addition to the $3$-symmetric spaces, without a Kählerian counterpart.

中文翻译：

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四维凯勒李群和准凯勒李群的几何

我们对四维拟凯勒李代数进行了分类，并研究了它们的几何形状，表明它们在半对称情况下是对称的或简调和特殊循环的。非半对称情况除了允许基本上两种不同的几何形状$3$-对称空间，没有凯勒对应空间。