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Solvable real rigid Lie algebras are not necessarily completely solvable [Les algèbres de Lie résolubles rigides réelles ne sont pas nécessairement complètement résolubles]

J. M. Ancochea Bermudez·R. Campoamor-Stursberg·L. Garcia Vergnolle
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Abstract

We show that a solvable real rigid Lie algebra is not completelt rigid, by constructing an example of minimal dimension where the external torus is not spanned by $ad$-semisimple derivations over $\mathbb{R}$. We analyze the real forms of nilradicals of solvable rigid Lie algebras in dimensions $n\leq 7$ and give the real classification for dimension 8.

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J. M. Ancochea Bermudez, R. Campoamor-Stursberg, L. Garcia Vergnolle. 2005-10-13. Solvable real rigid Lie algebras are not necessarily completely solvable [Les algèbres de Lie résolubles rigides réelles ne sont pas nécessairement complètement résolubles]. https://arxiv.org/abs/math/0510275

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