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The spin-1 matrices and the Gell-Mann matrices are pretty similar. Is there a way to get one set from the other?

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The spin-1 matrices arise from a homomorphism of groups SU(2) -> SU(3). In fact, it corresponds to the unique irreducible representation of SU(2) of dimension 3. Differentiating this homomorphism gives a map of Lie algebras, which sends the basis of Lie algebra su(2) into the span of the basis for su(3) (the Gell-Mann matrices).

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