Show that the Lorentz group commutation relations (13.20) are satisfied by the choices (K_{i}= pm frac{i}{2} sigma_{i})

Question:

Show that the Lorentz group commutation relations (13.20) are satisfied by the choices \(K_{i}= \pm \frac{i}{2} \sigma_{i}\) and \(J_{i}=\frac{1}{2} \sigma_{i}\), where the \(\sigma_{i}\) are Pauli matrices.

Data from 13.20

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