Realization of the Infinite-Dimensional 3-Algebras in the Calogero–Moser Model

We investigate realization of the infinite-dimensional 3-algebras in the classical Calogero–Moser model. In terms of the Lax matrix of the Calogero–Moser model and the Nambu 3-brackets in which the variables are the coordinates q_i, and canonically conjugate momenta p_i and the coupling parameter β are an extra auxiliary phase-space parameter, we present the realization of the Virasoro–Witt, w_∞ and SDiff(T²) 3-algebras, respectively.