Understanding Lie Algebra Operations: [A, B] and the meaning of ad

[romsofia]

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!

 

[Square]

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

 

[romsofia]

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.