特殊ユニタリ群
λ 4 = [ 0 0 1 0 0 0 1 0 0 ] λ 5 = [ 0 0 − i 0 0 0 i 0 0 ] λ 6 = [ 0 0 0 0 0 1 0 1 0 ] {\displaystyle \lambda _{4}={\begin{bmatrix}0&0&1\\0&0&0\\1&0&0\\\end{bmatrix}}\quad \lambda _{5}={\begin{bmatrix}0&0&-i\\0&0&0\\i&0&0\\\end{bmatrix}}\quad \lambda _{6}={\begin{bmatrix}0&0&0\\0&0&1\\0&1&0\\\end{bmatrix}}}
λ 7 = [ 0 0 0 0 0 − i 0 i 0 ] λ 8 = 1 3 [ 1 0 0 0 1 0 0 0 − 2 ] {\displaystyle \lambda _{7}={\begin{bmatrix}0&0&0\\0&0&-i\\0&i&0\\\end{bmatrix}}\quad \lambda _{8}={\frac {1}{\sqrt {3}}}{\begin{bmatrix}1&0&0\\0&1&0\\0&0&-2\\\end{bmatrix}}}
交換関係は
[ T a , T b ] = i ∑ c = 1 8 f a b c T c {\displaystyle [T_{a},T_{b}]=i\sum _{c=1}^{8}f_{abc}T_{c}}
となり、構造定数 f は
f 123 = 1 {\displaystyle f_{123}=1\,}