### ?

## R-matrix-valued Lax pairs and long-range spin chains

In this paper we discuss *R* -matrix-valued Lax pairs for sl *N* Calogero-Moser model and their relation to integrable quantum long-range spin chains of the Haldane-Shastry-Inozemtsev type. First, we construct the *R* -matrix-valued Lax pairs for the third flow of the classical Calogero-Moser model. Then we notice that the scalar parts (in the auxiliary space) of the *M* -matrices corresponding to the second and third flows have form of special spin exchange operators. The freezing trick restricts them to quantum Hamiltonians of long-range spin chains. We show that for a special choice of the *R* -matrix these Hamiltonians reproduce those for the Inozemtsev chain. In the general case related to the Baxter's elliptic *R* -matrix we obtain a natural anisotropic extension of the Inozemtsev chain. Commutativity of the Hamiltonians is verified numerically. Trigonometric limits lead to the Haldane-Shastry chains and their anisotropic generalizations.