Special Linear Lie Algebra

  • Thread starter heras1985
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  • #1
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Main Question or Discussion Point

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

Answers and Replies

  • #2
Welcome to PF.

What exactly have tried? A good point to start is citing the definition of "Special linear Lie algebra" and "simple".
 
  • #3
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Definition of simple:
L is called simple if it has no ideals except {0} and L.
I is an ideal of L if [tex]x\in L, y\in I \Rightarrow [x,y]\in I [/tex]
The matrices whose trace is 0 form the special linear lie algebra [tex]sl_n(\mathbb{C})[/tex]. 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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