This article is cited in 9 papers

Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems

A. V. Smirnov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We show a relation between systems of integrable tops on the algebras $sl(N,\mathbb C)$ and Calogero–Moser systems of $N$ particles. We construct classical Lax operators corresponding to these systems. We show that these operators are related to certain new trigonometric and rational solutions of the Yang–Baxter equations for the algebras $sl(N,\mathbb C)$ and give explicit formulas for $N=2,3$.

Keywords: integrable system, Euler–Arnold top, Yang–Baxter equation.

Received: 06.06.2008

DOI: 10.4213/tmf6319

 English version: Theoretical and Mathematical Physics, 2009, 158:3, 300–312

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