  We investigate the quantum Calogero-Moser model and reveal its hidden
symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large
$N$ limit, we note that these two infinite dimensional 3-algebras reduce to the
$w_{\infty}$ and special Virasoro-Witt 3-algebras which satisfy the fundamental
identity condition, respectively.
