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arXiv · 1602.07200

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

M. Ladra·K. K. Masutova·B. A. Omirov
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Abstract

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.

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M. Ladra, K. K. Masutova, B. A. Omirov. 2016-04-14. Solvable Leibniz algebra with non-Lie and non-split naturally graded filiform nilradical and its rigidity. https://arxiv.org/abs/1602.07200

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