Center of a Lie algebra

  • Thread starter Dogtanian
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  • #1
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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:
 

Answers and Replies

  • #2
matt grime
Science Advisor
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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.
 
  • #3
13
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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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