Let be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of consisting of nilpotent elements is contained in some Borel subalgebra. In this Note, we provide examples for each semisimple group G and for each of the torsion primes for G of nil subalgebras not lying in any Borel subalgebra of .
Soit l'algèbre de Lie d'un groupe algébrique linéaire semi-simple. Si l'on impose certaines conditions à la caractéristique du corps de définition, on peut montrer que toute sous-algèbre de ne contenant que des éléments nilpotents est contenue dans une sous-algèbre de Borel. Dans cette Note, nous donnons des exemples, pour chaque groupe semi-simple G et pour chaque nombre premier de torsion pour G, de sous-algèbres d'éléments nilpotents qui ne sont contenues dans aucune sous-algèbre de Borel de .
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@article{CRMATH_2009__347_9-10_477_0,
author = {Levy, Paul and McNinch, George and Testerman, Donna M.},
title = {Nilpotent subalgebras of semisimple {Lie} algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {477--482},
publisher = {Elsevier},
volume = {347},
number = {9-10},
year = {2009},
doi = {10.1016/j.crma.2009.03.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.015/}
}
TY - JOUR AU - Levy, Paul AU - McNinch, George AU - Testerman, Donna M. TI - Nilpotent subalgebras of semisimple Lie algebras JO - Comptes Rendus. Mathématique PY - 2009 SP - 477 EP - 482 VL - 347 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.015/ DO - 10.1016/j.crma.2009.03.015 LA - en ID - CRMATH_2009__347_9-10_477_0 ER -
%0 Journal Article %A Levy, Paul %A McNinch, George %A Testerman, Donna M. %T Nilpotent subalgebras of semisimple Lie algebras %J Comptes Rendus. Mathématique %D 2009 %P 477-482 %V 347 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.015/ %R 10.1016/j.crma.2009.03.015 %G en %F CRMATH_2009__347_9-10_477_0
Levy, Paul; McNinch, George; Testerman, Donna M. Nilpotent subalgebras of semisimple Lie algebras. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 477-482. doi : 10.1016/j.crma.2009.03.015. http://www.numdam.org/articles/10.1016/j.crma.2009.03.015/
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