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Question about SO(N) group generatorsby Einj
Tags: generators 
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#1
Jan2013, 05:19 AM

P: 321

Hi all. I have a question about the properties of the generators of the SO(N) group.
What kind of commutation relation they satisfy? Is it true that the generators λ are such that: $$\lambda^T=\lambda$$ ?? Thank you very much 


#2
Jan2113, 10:23 PM

P: 1,245

The commutators are complicated, in generalor too complicated for me.
Yes, the Lie algebra of SO(n) is the skewsymmetric matrices, which is the condition you wrote. That comes from differentiating a path of orthogonal matrices at the identity, or rather differentiating the equation that defines an orthogonal matrix. 


#3
Jan2113, 10:53 PM

P: 150

Notice, that the ndimensionality of SO(n) are triangle numbers in ℝ^{n} hopefully this can help you figure out a reason why, also I set a link to a video I think that might be able to help.
Link: http://www.youtube.com/watch?v=W6JWck4__Y Edit: Also may I ask why do you need to know this thing about the lie commutators in SO(n)? 


#4
Jan2213, 01:44 AM

P: 321

Question about SO(N) group generators



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