We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an abelian subalgebra of codimension 2. Here we explicitly construct an abelian ideal of codimension 2 in case of nilpotent Lie algebras.
1
Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria
2
Dep. Geometria y Topologia, Universidad de Sevilla, Sevilla, Spain
Dietrich Burde; Manuel Ceballos. Abelian Ideals of Maximal Dimension for Solvable Lie Algebras. Journal of Lie Theory, Tome 22 (2012) no. 3, pp. 741-756. http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a5/
@article{JOLT_2012_22_3_a5,
author = {Dietrich Burde and Manuel Ceballos},
title = {Abelian {Ideals} of {Maximal} {Dimension} for {Solvable} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {741--756},
year = {2012},
volume = {22},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a5/}
}
TY - JOUR
AU - Dietrich Burde
AU - Manuel Ceballos
TI - Abelian Ideals of Maximal Dimension for Solvable Lie Algebras
JO - Journal of Lie Theory
PY - 2012
SP - 741
EP - 756
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a5/
ID - JOLT_2012_22_3_a5
ER -
%0 Journal Article
%A Dietrich Burde
%A Manuel Ceballos
%T Abelian Ideals of Maximal Dimension for Solvable Lie Algebras
%J Journal of Lie Theory
%D 2012
%P 741-756
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a5/
%F JOLT_2012_22_3_a5
