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

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

2005-10-13

arxiv.org/abs/math/0510275v1

Mathematics

Representation Theory

8 pages, text in french

Scientific paper

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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