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Resumen:
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The goal in this article is to give a constructive method describing the n-dimensional rigid Lie algebras ?, with "rigid'' meaning, in the simplest sense, that every Lie algebra law sufficiently close to ? is isomorphic to it. The authors use Lie algebra results obtained by Goze via methods of nonstandard analysis, as well as the following theorem, due to R. Carles : For a law ? in Cn to be rigid, it must possess a semisimple inner derivation with integer eigenvalues. This reduces the problem to the study of a system of roots associated with this adjoint: Various nonrigidity criteria are given by properties of the system. The authors are then able to describe rigid laws both in arbitrary and in small dimensions; an example in C6 is completely illustrated and the 31 solvable rigid laws of dimension 8 are described
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