What exactly is Simple algebra of type $A_2$? I found that it has something to do with root systems, which I also don't really know what those are. Any idea?
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Thanks, but I still can't understand what is the definition. Specifically I need to prove that $sl(3,\mathbb R)$ is $A_2$. – TzurEl Jul 03 '16 at 16:11
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This is done in the duplicate, see the comments there: $\mathfrak{sl}(3)$, the Lie algebra of traceless $3\times 3$-matrices, is determined by its Cartan numbers, which are exactly the ones of $A_2$. Or said otherwise: Lie algebras of type $A_n$ are just the Lie algebras $\mathfrak{sl}(n+1)$ for all $n\ge 1$. – Dietrich Burde Jul 03 '16 at 16:15
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It is best to first post a Question about the definition of something, rather than charging ahead with a problem centering on a definition you do not understand. When you ask a Question, Readers need to rely on you to know what it is you are asking. – hardmath Jul 03 '16 at 17:25