Lie algebra (quick question)

  • Thread starter romsofia
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Sorry for such a simple question, usually I'd go to my physics teacher for help on this question, but it's break and I really don't know the answer.

I'm currently studying from an online book (http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) and on the bottom of page 8 he states "Let ad A denote the operation of bracketing on the left by A, so adA(B) := [A, B]"

Is this implying [A,B] is the lie bracket (pretty sure this is the case, but better to ask then mislead myself!), and what does the ad mean (nothing comes to mind)?

Thanks for the help!
 

Answers and Replies

  • #3
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Yes, [A,B] is in this case the Lie brackets since it got defined by the writer in equation (1.1) earlier on the same page.

The ad stands for adjoint I believe. You can read more about the adjoint endomorphism on wikipedia: http://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra
That would make sense for it be adjoint endomorphism after a quick skim of the wikipedia page (however, I have never heard of the term)! Thanks for you time.
 

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