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Is it possible to construct a basis of $su(4)$ such that for any pair of elements of that basis we satisfy the following property, $$\{f_{\mu},f_{\nu}\}=2\delta_{\mu \nu}f_{\mu}^2,$$ where $\{A,B\}=AB+BA$? This is just an extension of the well-known basis of $su(2)$ given by the Pauli's matrices which satisfies the mentioned property.

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    $\begingroup$ You can't multiply elements of an algebra or compute the anticommutator. Do you mean, is there a representation of $su(4)$ in which there exists a basis where your equation is true? $\endgroup$
    – Prahar
    Sep 12, 2021 at 9:51
  • $\begingroup$ No. Use this to prove it. $\endgroup$ Sep 12, 2021 at 12:52

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