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Ancochea Bermúdez, José María and Campoamor Stursberg, Otto Ruttwig and García Vergnolle, Lucía
(2006)
*Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical.*
International Mathematical Forum, 1
(5-8).
pp. 309-316.
ISSN 1312-7594

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Official URL: http://www.m-hikari.com/imf-password/5-8-2006/campoamorIMF5-8-2006.pdf

## Abstract

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

Item Type: | Article |
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Uncontrolled Keywords: | Lie algebra, Levi decomposition, radical |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 20726 |

Deposited On: | 09 Apr 2013 18:18 |

Last Modified: | 12 Dec 2018 15:13 |

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