Source: Anderson, Principles of Relativity Physics p. 13, prob. 1.4 "Reparametrize the rotation group by taking, as new infinitesimal parameters, ε1 = ε23, ε2 = ε31, and ε3 = ε12 and calculate the structure constants for these parameters." My assumptions: (1) The εij mentioned in the problem are the infinitesimal Cartesian parameters of the 3-D rotation group such that εij = -εji, and yi = xi + Σjεijxj, where x is the original point and y is the transformed point. (2) To generalize this to non-Cartesian coordinates and still maintain the Lie group-ness, the transformation takes the general form: yi = xi + Σkεkfki(x) where the fki(x) satisfy the following condition. (3) The request for structure constants is a request for constants ckmn such that: yi = xi + ΣkΣmΣn(εBmεAn - εAmεBn)ckmnfki(x) (4) The parameters εk are the non-Cartesian parameters, and so, they should multiply some functions fki(x), and these functions determine the structure constants. My problem with understanding: I don't know how to find the fki(x). I have: Σjεijxj = Σkεkfki(x) but I don't see how this tells me fik(x). Am I supposed to assume some kind of orthogonality or something?