# One dimensional lie algebra's

1. May 4, 2015

### PsychonautQQ

I just read that the bi-linear bracket operation on any one dimensional lie algebra is abelian (vanishing) because of the anti-symmetry property. I'm not understanding the connection, can anyone enlighten me?

2. May 4, 2015

### fzero

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.