Integrable systems associated with elliptic algebras
Alexander Odesskii
University of Manchester, UKVladimir Rubtsov
Université d’Angers, France
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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.