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I'm reviewing my Group theory notes at the moment. I have a few questions.
1)what is the "connected component of the identity"? (How would you go about working this out?)
2)Why is Lie(SO(n))=Lie(O(n))?
3)Why is the SU(2) Lie group isomorphic to a sphere in 3D?
1)what is the "connected component of the identity"? (How would you go about working this out?)
2)Why is Lie(SO(n))=Lie(O(n))?
3)Why is the SU(2) Lie group isomorphic to a sphere in 3D?