Journal of Lie Theory

no. 4
Commutators and Cartan Subalgebras in Lie Algebras of Compact Semisimple Lie Groups
Journal of Lie Theory, Volume 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.
DOI: 10.5802/jolt.980
Classification: 22E60, 20F12
Keywords: Semisimple Lie Algebras, commutators, Goto's Theorem, Cartan subalgebras 
@article{JOLT_2017_27_4_a6,
     author = {J. Malkoun and N. 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},
     doi = {10.5802/jolt.980},
     zbl = {1383.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.980/}
}
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J. Malkoun; N. Nahlus. Commutators and Cartan Subalgebras in Lie Algebras of Compact Semisimple Lie Groups. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1027-1032. doi: 10.5802/jolt.980

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