Concerning a Lie algebra defined by the structure constants: keep in mind 
this is a way often used in Physics, which is not very rigorous. Structure 
constants define an equivalence class of bases in a Lie algebra.

For example, consider a Lie algebra with two generators: *A, B*. If you 
define *X = 2*A - 3*B, Y = A + B*, then *X *and *Y* are still generators, 
but will have generally different structure constants.

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