2026-06-29T07:25:49Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/505622024-07-16T15:21:56Zcom_20.500.14352_14col_20.500.14352_15

Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical Ancochea Bermúdez, José María Campoamor Stursberg, Otto-Rudwig García Vergnolle, Lucía 512.554.3 Lie algebra Levi decomposition radical Álgebra 1201 Álgebra 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 filiform Lie algebra of dimension n = dim r. This leads to a contradiction, since no such indecomposable algebra snr with r = fn exists Universidad Complutense de Madrid Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T10:34:05Z 2023-06-20T10:34:05Z 2006 journal article https://hdl.handle.net/20.500.14352/50562 1312-7594 eng PR1/05-13283 open access application/pdf Hikari