Commutators and Cartan subalgebras in Lie algebras of compact semisimple Lie groups

Joseph Malkoun, Nazih Nahlus

First we give a new proof of Goto's theorem for Lie algebras of compact semisimple Lie groups using Coxeter transformations. Namely, every $x$ in $L=\mathrm{Lie}(G)$ can be…