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The usual action of $fg$ on $u⊗v$, where $f,g$ are elements in the Universal Enveloping Algebra $U(G)$ of a Lie algebra $G$ and $u,v$ are elements of a representation $V$ of $G$, is given by $fg(u⊗v)=fgu⊗v+fu⊗gv+gu⊗fv+u⊗fgv$, right? How to state this fact for $V^{\otimes n}$, i.e. $fg$ acting on $u⊗v$, where $u=⊗_{i=1}^{n-k} u_i$ and $v=\otimes_{i=1}^k v_i$, for each $k=1,...,n−1$? Thanks,

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