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Time translations are generated by $H$, as expected. The generator for Gallilean boosts $\vec{K}$ is related to the CM operator $\vec{R}=1/M\sum_i m_i\vec{x}_i$, $\vec{K}=M\vec{R}$. See http://en.wikipedia.org/wiki/Schr%C3%B6dinger_group for some references.