Let $(e_1,\dots,e_n)$ be an ordered $k$-basis of $\mathfrak g$, and let $(e^1,\dots,e^n)$ be the $B$-[dual basis](/theorems/414), characterized by
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\begin{align*}
B(e_i,e^j)=\delta_i^j
\end{align*}
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for all $i,j\in\{1,\dots,n\}$. If $U(\mathfrak g)$ denotes the universal enveloping algebra of $\mathfrak g$, with multiplication written by juxtaposition, then the element