标题： 可解的莱布尼茨代数，具有非李且非分裂的自然分次的拟幂零根及其刚性 显示英文标题

标题： Solvable Leibniz algebra with non-Lie and non-split naturally graded filiform nilradical and its rigidity

摘要： 复杂可解李布尼茨代数的描述，其幂零根是一个自然分次的拟幂零代数，已经为人所知。 不幸的是，在该描述中存在一个错误。 具体来说，当具有幂零根$F_n^1$的可解李布尼茨代数的维数等于$n+2$时，曾断言不存在这样的代数。 然而，我们找到了一个唯一的$(n+2)$维可解李布尼茨代数，其幂零根为$F_n^1$。 此外，我们建立了该代数自身系数的二阶上同调群的平凡性，这表明其刚性。 显示英文摘要

摘要： The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable Leibniz algebra with nilradical $F_n^1$ is equal to $n+2$, it was asserted that there is no such algebra. However, it was possible for us to find a unique $(n+2)$-dimensional solvable Leibniz algebra with nilradical $F_n^1$. In addition, we establish the triviality of the second group of cohomology for this algebra with coefficients in itself, which implies its rigidity.