On the conjugacy theorem of Cartan subalgebras.
Consider a finite-dimensional Lie algebra over an algebraically closed field of characteristic 0. Recall that a nilpotent subgroup which equals its normalizer is called Cartan subalgebra. It is well-known that in our context all Cartan subalgebras are conjugate. The authors give a new elementary, direct proof of this theorem, which fits into the context of \textit{N.~Bourbaki}, Groupes et algèbres de Lie, Ch.~7, 8 Herman, Paris (1975; Zbl 0329.17002). They also reprove that all Borel subalgebras (maximal solvable subalgebras) are conjugate.
scientific article; zbMATH DE number 1874209