What is the simplicity of the Special Linear Lie Algebra?

heras1985
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Hi,
Show that the Special linear Lie algebra is simple.
I tried it with induction but without result.
 
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What exactly have tried? A good point to start is citing the definition of "Special linear Lie algebra" and "simple".
 
Definition of simple:
L is called simple if it has no ideals except {0} and L.
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).
 
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