# Possible basis for Lie algebra $su(4)$

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.

• 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? Sep 12, 2021 at 9:51
• No. Use this to prove it. Sep 12, 2021 at 12:52