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 by José Marı́a Ancochea Bermúdez, Bermudez, J. M. Ancochea, Rutwig Campoamor-Stursberg +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0510275

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 ℝ. We analyze the real forms of nilradicals of solvable rigid Lie algebras in dimensions n≤ 7 and give the real classification for dimension 8.

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