# Lie bracket of differential operators

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Let $M$ be a differential manifold and $D_1,D_2$ be differential operators from $C^\infty(M)$ to $C^\infty(M)$. The Lie bracket of $D_1$ and $D_2$ denoted $[D_1,D_2]$ is defined as the following differential operator:
$D_1 \circ D_2 - D_2 \circ D_1$