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Show that the Special linear Lie algebra is simple.

I tried it with induction but without result.

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- Thread starter heras1985
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- #1

- 8

- 0

Show that the Special linear Lie algebra is simple.

I tried it with induction but without result.

- #2

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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).

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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