It seems to me, I could be wrong, that the toral sub algebra goes against the following rules:
For a semisimple Lie algebra:
If the killing form is nondegenerate the Lie algebra is semi simple-> the toral algebra is nilpotent
If the lie algebra is abelian the killing form is degenerate-> contradicting the previous statement.
Can anyone explain why? And if I am correct, the toral sub algebra of a semisimple Lie algebra is not an ideal.