Why is the bi-linear bracket operation on a one-dimensional Lie algebra abelian?

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I just read that the bi-linear bracket operation on anyone dimensional lie algebra is abelian (vanishing) because of the anti-symmetry property. I'm not understanding the connection, can anyone enlighten me?
 
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If the Lie algebra is one-dimensional, all of the elements are multiples of a single generator, say ##L##. Any bracket is therefore proportional to ##[L,L]=0## due to antisymmetry.
 

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