# Question about SO(N) group generators

by Einj
Tags: generators
 P: 153 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
 P: 826 The commutators are complicated, in general--or too complicated for me. Yes, the Lie algebra of SO(n) is the skew-symmetric 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.
 P: 150 Notice, that the n-dimensionality of SO(n) are triangle numbers in ℝn 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)?
P: 153

## Question about SO(N) group generators

 Quote by homeomorphic Yes, the Lie algebra of SO(n) is the skew-symmetric 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.
Thank you very much! That solves some problems!

 Quote by Tenshou Edit: Also may I ask why do you need to know this thing about the lie commutators in SO(n)?
I am working on the SO(N) symmetry of a $\lambda \phi^4$ theory in QFT and I need the exact expression of the commutator of two conserved charges, so I need to know the commutator of the generators.

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