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The goal is to prove directly that $\mathfrak{sl}(n,\Bbb C)$ is a simple Lie algebra for $n \ge 2$

So far I'm trying to think of ways to show that there are no non-trivial ideals (definition of simple) for $\mathfrak{sl}(n,\Bbb C)$, where $\mathfrak{sl}(n,\Bbb C)$ is the collection of all matrices which have trace $= 0$.

I'm still trying to wrap my head around Lie algebras, so any help is appreciated.

Daniele Tampieri
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Rusk
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  • quick googling yields https://www.math.cuhk.edu.hk/~plyung/simplicity_sln.pdf some linear algebra knowledge required, but the proof is more or less self-contained – AlvinL Nov 26 '19 at 08:18
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    Here's a link to a proof for the case $n=2$: https://math.stackexchange.com/a/1409941/55622 – Oliver Jones Nov 26 '19 at 08:45

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