I am trying to understand the proof of the following result from Humphreys Lie Algebra book:
Let $L$ be a semisimple complex Lie Algebra.Let $H$ be Maximal toral subalgebra of $H$,Let $C_L(H)$ denote the centralizer of $H$ in $L$.Show that $C_L(H)=H$.
The proof given in Humphreys book on page $36$ does not seem 'natural' to me,and i am having hard time with the steps of proof.I think i understand the proof but if someone will ask me to reproduce the proof i dont think i will to able to do so. Can someone give me a better reference or outline a "natural' proof or explain me the Humphreys proof properly.