# Generalized model of interacting integrable tops

## TL;DR

This paper introduces a new family of classical integrable systems modeling interacting ${
m gl}_N$ tops, extending previous models with a construction based on the ${
m GL}_N$ $R$-matrix, and providing explicit Lax pairs and $r$-matrices.

## Contribution

The paper develops a generalized integrable model of interacting tops using the ${
m GL}_N$ $R$-matrix, extending known elliptic top models and connecting to spin Calogero-Moser systems.

## Key findings

- Constructed a family of integrable models with explicit Lax pairs.
- Extended the model to include anisotropic spin exchange operators.
- Reproduced the spin Calogero-Moser model in the $N=1$ case.

## Abstract

We introduce a family of classical integrable systems describing dynamics of $M$ interacting ${\rm gl}_N$ integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the ${\rm GL}_N$ $R$-matrix satisfying the associative Yang-Baxter equation. The obtained systems can be considered as extensions of the spin type Calogero-Moser models with (the classical analogues of) anisotropic spin exchange operators given in terms of the $R$-matrix data. In $N=1$ case the spin Calogero-Moser model is reproduced. Explicit expressions for ${\rm gl}_{NM}$-valued Lax pair with spectral parameter and its classical dynamical $r$-matrix are obtained. Possible applications are briefly discussed.