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Define a left-normed commutator $[a_1, a_2, \\dots , a_n]$ inductively by $[a_1, a_2] = a_1 a_2 - a_2 a_1$, $[a_1, \\dots , a_{n-1}, a_n] = [[a_1, \\dots , a_{n-1}], a_n]$ $(n \\ge 3)$. 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