%0 Journal Article
%A Ancochea Bermúdez, José María
%A Campoamor Stursberg, Otto-Rudwig
%A García Vergnolle, Lucía
%T Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
%D 2006
%@ 1312-7594
%U https://hdl.handle.net/20.500.14352/50562
%X Let g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform nilpotent Lie algebra. The proof uses the fact that any Lie algebra g = snr with filiform radical would degenerate (even contract) to the Lie algebra snfn, where fn is the standard graded filiformLie algebra of dimension n = dim r. This leads to a contradiction, since no such indecomposable algebra snr with r = fn exists
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