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comment What is the structure of $SO(3)$ and its Lie Algebra?
Ah that's nice. Of course, the derivative of the commutator map gives one on the corresponing tangent spaces. But then the usual notation of your $(dC_a)_e$ map, i.e. $(dC_a)_e (g) = aga^{-1}$ is a purely formal expression and does a priori not correspond to actual products. But concerning $SO(3)$, I am very well aware that $SO(3)$ is the group of rotations preserving euclidian norm and orientation, but I wondered if there is a nice presentation of this group. It certainly is formally ok to let it be the group of automorphisms of a real 3-d oriented inner prod space, but a bit unsatisfying
Nov
18
asked What is the structure of $SO(3)$ and its Lie Algebra?