Trigonometric integrable tops from solutions of associative Yang-Baxter equation (Q2001962)

The aim of the article is to construct classical relativistic integrable tops from quantum non-dynamical trigonometric \(R\)-matrices satisfying associative Yang-Baxter equations. These \(R\)-matrices are expressed via the associative Belavin-Drinfeld structure and have properties of skew-symmetry and unitarity. Their classification, based on the classification of bundles over elliptic curves, is shortly reviewed. It is shown that the \(R\)-matrices considered here produce quadratic Poisson structures of Sklyanin-type and they can be put in correspondence with relativistic tops. Relations with Ruijsenaars-Schneider and Calogero-Moser-Sutherland models are investigated.