Integrable systems and loop coproducts

Abstract

We present a generalization of a framework for the construction of classical integrable systems that we call loop coproduct formulation (Musso 2010 J. Phys. A: Math. Theor. 43 434026). In this paper, the loop coproduct formulation includes systems of Gelfand–Tsetlin type, the linear r-matrix formulation, the Sklyanin algebras, the reflection algebras, the coalgebra symmetry approach and some of its generalizations as particular cases, showing that all these apparently different approaches have a common algebraic origin. On the other hand, all these subcases do not exhaust the domain of applicability of this new technique, so that new possible directions of investigation do naturally emerge in this framework.