Normalisers of Abelian Ideals of a Borel Subalgebra and Z-Gradings of a Simple Lie Algebra
Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 659-672
Voir la notice de l'article provenant de la source Heldermann Verlag
Let g be a simple Lie algebra and Ab the poset of all abelian ideals of a fixed Borel subalgebra of g. If a is an element of Ab, then the normaliser of a is a standard parabolic subalgebra of g. We give an explicit description of the normaliser for a class of abelian ideals that includes all maximal abelian ideals. We also elaborate on a relationship between abelian ideals and Z-gradings of g associated with their normalisers.
Classification :
17B20, 17B22, 20F55
Mots-clés : Root system, Borel subalgebra, minuscule element, abelian ideal
Mots-clés : Root system, Borel subalgebra, minuscule element, abelian ideal
Affiliations des auteurs :
Dmitri I. Panyushev 1
Dmitri I. Panyushev. Normalisers of Abelian Ideals of a Borel Subalgebra and Z-Gradings of a Simple Lie Algebra. Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 659-672. http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a2/
@article{JOLT_2016_26_3_a2,
author = {Dmitri I. Panyushev},
title = {Normalisers of {Abelian} {Ideals} of a {Borel} {Subalgebra} and {Z-Gradings} of a {Simple} {Lie} {Algebra}},
journal = {Journal of Lie Theory},
pages = {659--672},
year = {2016},
volume = {26},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a2/}
}