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Special Linear Lie Algebra

  1. Apr 29, 2008 #1
    Show that the Special linear Lie algebra is simple.
    I tried it with induction but without result.
  2. jcsd
  3. Apr 29, 2008 #2
    Welcome to PF.

    What exactly have tried? A good point to start is citing the definition of "Special linear Lie algebra" and "simple".
  4. Apr 29, 2008 #3
    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).
    Last edited: Apr 29, 2008
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