Let L be a 3-dimensional vector space over k with basis x,y,z. Given L an anti-commutative algebra structure by setting $[x,y]=z,[y,z]=x,[z,x]=y$
Prove that L is a simple Lie algebra.
So L is simple if 0 or L are the only ideals of L.
So assume, I is an ideal s.t. that $0 \not = v \in I$ and is not L. I suppose you would start with $v=ax+by+cz$ and then show what? that you can get everything?
I'm a bit unsure what to do, can someone give me a hint?