We describe all central extensions of all 3-dimensional nontrivial complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional nontrivial complex Zinbiel algebras and a full classification of 5-dimensional nontrivial complex Zinbiel algebras with 2-dimensional annihilator, which gives the principal step in the algebraic classification of 5-dimensional Zinbiel algebras.

中文翻译：

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3 维 Zinbiel 代数的中心扩展

我们描述了所有 3 维非平凡复 Zinbiel 代数的所有中心扩展。作为推论，我们有 4 维非平凡复 Zinbiel 代数的完整分类和具有 2 维湮灭器的 5 维非平凡复 Zinbiel 代数的完整分类，这给出了 5 维 Zinbiel 代数代数分类的主要步骤.