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From Braided Geometry to Integrable systems.

Le : 05/10/2011 11h00
Par : Dimitri GUREVICH (LAMATH Université de Valenciennes)
Lieu : I 103
Lien web :
Résumé : By Braided Geometry I mean a theory dealing with braidings (i.e. solutions of the Quantum Yang-Baxter Equation) playing the role of the usual flip or (super-flip). The main object of Braided Geometry is the so-called Reflection Equation Algebra associated to a given braiding. This algebra can be treated as an analog of the enveloping algebra U(gl(m|n)). Besides, for a matrix coming in its definition there is an analog of the Cayley-Hamilton identity. A version of partial derivatives can be defined on this algebra as well. I plan to describe in my talk a way of getting an analog of the Calogero-Moser system by using the mentioned properties of the Reflection Equation Algebra.