Abstract. We construct new integrable systems (IS), both classical and quantum, associated with elliptic algebras. Our constructions are based both on a construction of commuting families in skew fields and on properties of the elliptic algebras and their representations. We give some examples showing how these IS are related to previously studied systems. Introduction. This paper is an attempt to establish a direct connection between two close subjects of modern Mathematical Physics: integrable systems (IS) and elliptic algebras. More precisely, we construct IS on a large class of elliptic algebras. We will start with a short account of the subject of the story and then we will briefly describe the IS’s under consideration.
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