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One dimensional lie algebra's

  1. May 4, 2015 #1
    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. jcsd
  3. May 4, 2015 #2


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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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