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Bihamiltonian structures from non-commutative geometry

Le : 22/03/2017 14h00
Par : Alberto Tacchella (Gênes)
Lieu : I 001
Lien web :
Résumé : Double Poisson structures have been defined by Van den Bergh as an analogue of Poisson structures on a generic associative algebra. It is then natural to interpret a pair of compatible double Poisson brackets as a non-commutative bihamiltonian structure. In this talk I will show how to obtain such compatible double Poisson structures starting from a Nijenhuis operator on the path algebra of a quiver, generalizing a well-known construction (due to Kosmann-Schwarzbach and Magri) that works in the commutative setting. This formalism can be used to recover a bihamiltonian formulation for various integrable systems of Calogero-Moser type.