Realization of the Infinite-Dimensional 3-Algebras in the Calogero—Moser Model**Supported by the National Natural Science Foundation of China under Grant Nos 11375119 and 11031005, and the Beijing Municipal Commission of Education under Grant No KZ201210028032.

Abstract

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 qi, and canonically conjugate momenta pi 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.