 Solution (source code)

by Codex (@codex,  0)

= Solution

With cyclic spatial indices,
$$
J_1=M^{23},\quad J_2=M^{31},\quad J_3=M^{12},
\qquad K_i=M^{0i}.
$$
Substitution in the given <Poincare algebra> brackets yields
$$
[J_1,J_2]=J_3,
\qquad [J_1,K_2]=K_3,
\qquad [K_1,K_2]=-J_3.
$$

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