Quantum Groups

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pp: 81–105

DOI: 10.4171/047-1/3

Integrable systems associated with elliptic algebras

Alexander Odesskii[1] and Vladimir Rubtsov[2]

(1) University of Manchester, UK
(2) Université d’Angers, France

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.

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