U(N) and SO(N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups?
Lie Algebra of U(N) and SO(N)
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group-theory
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1If you have a copy of John Lee's book on Smooth manifolds, you can find the important details of these computations in chapter 8. I don't have my book with me right now, but I'll update with specific page information tomorrow. – 2012-10-09