Question about SO(N) group generators

Einj

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

homeomorphic

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.

Tenshou

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)?

Einj

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 [itex]\lambda \phi^4[/itex] 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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Einj	Question about SO(N) group generators Tweet 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

homeomorphic	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.

Tenshou	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)?