 Solution (source code)

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= Solution

A <Lie bracket> is bilinear, antisymmetric, and satisfies the <Jacobi identity>. For a basis $T_a$,
$$
[T_a,T_b]=f_{ab}{}^cT_c.
$$
The <structure constant of a Lie algebra> coefficients satisfy $f_{ab}{}^c=-f_{ba}{}^c$ and $f_{ab}{}^df_{dc}{}^e+f_{bc}{}^df_{da}{}^e+f_{ca}{}^df_{db}{}^e=0$.

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