Abstract In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial.

中文翻译：

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一些上同调刚性可解莱布尼茨代数

摘要 本文描述了可解的莱布尼茨代数，其一维理想的商代数是秩等于其幂零根特征序列长度的李代数。我们证明了这样的莱布尼茨代数是唯一的和无心的。还证明了伴随表示中具有系数的代数的第一和第二上同调群是微不足道的。