Definition of rank for compact semisimple Lie group

Question

Let $G$ be a compact semisimple Lie group. I have found to different definitions of its rank: One of them defined the rank of the Lie group to be the dimension of a maximal torus. The other definition defined the rank to be the dimension of a Cartan subalgebra in the Lie algebra. Do these definitions coincide?

Answer 1

For semisimple Lie algebras, a Cartan subalgebra is a maximal abelian subalgebra, i.e., a maximal torus. So the definitions coincide.