# Semisimple elements of a lie algebra

Let $G\subset GL_n(\mathbb{C})$ be an algebraic group of dimension n, and let $\mathfrak{g}$ its Lie algebra.Is there a relations between the maximal number of independent semisimple elements of $G$ and the maximal number of independent semisimple elements $\mathfrak{g}$?

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What is "independent" in either case? –  doug Mar 10 '11 at 12:39
independent = linearly independent. sorry. –  Michele Torielli Mar 10 '11 at 14:21
Linear independence doesn't make sense for elements of a group. Perhaps you mean to ask what the relation is between the dimension of a maximal subalgebra consisting of semisimple elements (a maximal toral subalgebra) and the dimension of a maximal algebraic subgroup consisting of semisimple elements (a maximal torus). –  mephisto Mar 10 '11 at 18:52