Algebraic extensions of Gaudin models

Abstract

We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear $r$-matrix structure. We give a general construction involving rational, trigonometric and elliptic solutions of the classical Yang-Baxter equation. Two particular examples are explicitly considered: the rational Lagrange chain and the trigonometric one. In both cases local variables of the models are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting tops.