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I have been asked to prove that an algebra with only two generators can not be simple. I have thought about it and have tried to show that one of the two structure constants go to zero in the Lie algebra condition that [xi,xj]=sumoverk Cijkxk , but I can't find any way to show that (using the Bianci Identity, for example), and perhaps I am thinking about it the wrong way. I have also tried to think about it logically - perhaps it contains the identity for some reason and any algebra containing the identity is not simple.

I would appreciate any hints people might give me.

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# Two generators

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