Impacto
Downloads
Downloads per month over past year
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
![]() Preview |
PDF
99kB |
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 |
---|---|
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 |
Origin of downloads
Repository Staff Only: item control page