Does a a semisimple element x exist in mathfrak?

Add Comment

Tutor's Answer

(Top Tutor) Studyfaq Tutor
Therefore there exists a semisimple element x in mathfrak{g}. Consider S={lambda x|lambda in mathbb{C}}. By section 1.7 this is Abelian. Now either S is maximal, or we can find elements that commute with x and are themselves semisimple. So we can continually add these elements to form a basis of our Cartan Subalgebra. This process must terminate due to the finite dimensional nature of mathfrak{g}, so we can have at most Dim(mathfrak{g}) elements to form the basis of our Cartan subaglebra. end{proof} begin{framed} begin{theorem} Let G be a Lie group with semisimple Lie...
Completed Work