Abstract We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13 ). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15 ). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras.

中文翻译：

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幂零终代数的代数和几何分类

摘要 我们给出了 4 维复幂零终端代数的代数和几何分类。具体来说，我们发现，到同构为止，4维幂零终端（非莱布尼茨）代数有41个一参数族，4维幂零终端（非莱布尼茨）代数有18个二参数族，2个三-4 维幂零终端（非莱布尼茨）代数的参数族，辅以 21 个额外的同构类（见定理 13）。相应的几何变体的维数为 17，分解为 3 个不可约分量，这些分量由一参数代数族、二参数代数族和三参数代数族的 Zariski 闭包确定（见定理 15）。特别是，没有严格的 4 维复幂零终代数。