Abstract This article is devoted to n-dimensional nilpotent finite-dimensional evolution algebras with maximal index of nilpotency. We are able to find full invariants of these algebras which allows us to classify them. Furthermore, we explicitly describe its associative enveloping algebras. Moreover, we give an affirmative answer to the question: is it possible to extend a given derivation of the nilpotent evolution algebra to its enveloping algebra.

中文翻译：

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幂零演化代数的分类及其推导的扩展

摘要 本文致力于研究具有极大幂零指数的 n 维幂零有限维演化代数。我们能够找到这些代数的完整不变量，这使我们能够对它们进行分类。此外，我们明确地描述了它的关联包络代数。此外，我们对这个问题给出了肯定的回答：是否有可能将幂零演化代数的一个给定推导推广到它的包络代数。