Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical
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 d...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/50562 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/50562 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.554.3 Lie algebra Levi decomposition radical Álgebra 1201 Álgebra |
| Sumario: | 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 |
|---|