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Natural super-commutative structures in the geometry of integrable systems

Le : 08/10/2013 11h15
Par : Joseph Krasilschik (Independant University of Moscow, Russia)
Lieu : I 103
Lien web :
Résumé : Integrability properties of partial differential equations (existence of Poisson and/or symplectic structures, recursion operators, etc.) are closely related to the geometry of the so-called tangent and cotangent coverings to the equation at hand. The total spaces of these coverings are natural to be understood as supermanifolds, while Poisson structures and recursion operators become odd vector fields on these supermanifolds with the Schouten and Nijenhuis brackets playing the role of the supercommutator.