This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension 15 and decomposes into 3 irreducible components determined by the Zariski closures of two one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid 4-dimensional complex nilpotent left symmetric algebras.

中文翻译：

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幂等左对称代数的代数和几何分类

本文致力于复杂的4维幂等左对称代数的完整代数和几何分类。相应的几何变体的尺寸为15，并分解为3个不可约分量，该分量由两个单参数代数族和两个参数代数的Zariski闭包确定（请参见定理B）。特别是，没有刚性的4维复幂等左对称代数。