Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical

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Ancochea Bermúdez, José María and Campoamor-Stursberg, Rutwig 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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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
Uncontrolled Keywords:Lie algebra, Levi decomposition, radical
Subjects:Sciences > Mathematics > Algebra
ID Code:20726
Deposited On:09 Apr 2013 18:18
Last Modified:27 Sep 2022 11:21

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