1Dept. of Mathematics and Statistics, Notre Dame University, Louaize, Zouk Mikael, Lebanon 2Dept. of Mathematics, Faculty of Arts and Sciences, American University of Beirut, Beirut, Lebanon
Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1027-1032
Short proofs are given of the following facts concerning the Lie algebra g of a compact semisimple Lie group. (1) Any element in g is a commutator bracket of some two elements of g. (2) Given a Cartan subalgebra h of g, there exists a Cartan subalgebra h' which is orthogonal to h. Moreover, as a Corollary, we obtain the known fact that any element in g is conjugate to some element in the orthogonal complement of h.
1
Dept. of Mathematics and Statistics, Notre Dame University, Louaize, Zouk Mikael, Lebanon
2
Dept. of Mathematics, Faculty of Arts and Sciences, American University of Beirut, Beirut, Lebanon
Joseph Malkoun; Nazih Nahlus. Commutators and Cartan Subalgebras in Lie Algebras of Compact Semisimple Lie Groups. Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1027-1032. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a6/
@article{JOLT_2017_27_4_a6,
author = {Joseph Malkoun and Nazih Nahlus},
title = {Commutators and {Cartan} {Subalgebras} in {Lie} {Algebras} of {Compact} {Semisimple} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {1027--1032},
year = {2017},
volume = {27},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a6/}
}
TY - JOUR
AU - Joseph Malkoun
AU - Nazih Nahlus
TI - Commutators and Cartan Subalgebras in Lie Algebras of Compact Semisimple Lie Groups
JO - Journal of Lie Theory
PY - 2017
SP - 1027
EP - 1032
VL - 27
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a6/
ID - JOLT_2017_27_4_a6
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%J Journal of Lie Theory
%D 2017
%P 1027-1032
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a6/
%F JOLT_2017_27_4_a6
