Expressing a Tensor Permutation Matrix $p^{\otimes n}$ in Terms of the Generalized Gell-Mann Matrices

We have shown how to express a tensor permutation matrix $p^{\otimes n}$ as a linear combination of the tensor products of the $p\times p$-Gell-Mann matrices. We have given the expression of a tensor permutation matrix $2\otimes 2 \otimes 2$ as a linear combination of the tensor products of the Pauli matrices.