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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!