# Special Linear Lie Algebra

Hi,
Show that the Special linear Lie algebra is simple.
I tried it with induction but without result.

I is an ideal of L if $$x\in L, y\in I \Rightarrow [x,y]\in I$$
The matrices whose trace is 0 form the special linear lie algebra $$sl_n(\mathbb{C})$$. The special linear lie algebra is the lie algebra of the special linear group (this group is form by the matrices whose determinant is 1).