I've heard it said that the commutation relations of the generators of a Lie algebra determine the multiplication laws of the Lie group elements.(adsbygoogle = window.adsbygoogle || []).push({});

I would like to prove this statement for ##SO(3)##.

I know that the commutation relations are ##[J_{i},J_{j}]=i\epsilon_{ijk}J_{k}##.

Can you suggest a possible next step for showing how this can be used to determine the multiplication law for ##SO(3)##?

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# Lie group multiplication and Lie algebra commutation

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