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Center of a Lie algebra

  1. Mar 13, 2005 #1
    OK, can someone please tell if 0 (zero) would belong to the center of a Lie algebra.

    By center I mean for a Lie algebra L
    center(L) = { z in L : [z,x]=0 for all x in L}

    I think it should, but I'm not too sure...I'm surely confusing myself somewhere along the line, as this shouldn't be too difficult to say either way... :uhh:
  2. jcsd
  3. Mar 13, 2005 #2

    matt grime

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    So you're asking is [0,x] zero for all x? The answer is "of course": [ ] is linear and 0t=0 for all scalars t.
  4. Mar 13, 2005 #3
    Thanks. :biggrin:
    I thought it was right, but I just couldn't quite convinse myself...I thought it was quite obvious... :grumpy:
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