%0 Journal Article
%A Goze, Michel
%A Ancochea Bermúdez, José María
%T Algèbres de Lie rigides
%D 1985
%@ 0019-3577
%U https://hdl.handle.net/20.500.14352/64827
%X The goal in this article is to give a constructive method describing the n-dimensional rigid Lie algebras μ, with "rigid'' meaning, in the simplest sense, that every Lie algebra law sufficiently close to μ 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 μ 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
%~