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oai:docta.ucm.es:20.500.14352/648272025-02-21T16:34:50Zcom_20.500.14352_14col_20.500.14352_15

Algèbres de Lie rigides Goze, Michel Ancochea Bermúdez, José María 512.554.3 rigid Lie algebras solvable Lie algebras of dimension eight nonstandard method cohomology Álgebra 1201 Álgebra 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 Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-21T02:05:30Z 2023-06-21T02:05:30Z 1985 journal article https://hdl.handle.net/20.500.14352/64827 0019-3577 metadata only access Koninklijke Nederlandse Akademie van Wetenschappen