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Elements of quantum geometry on U(gl(m)) -background

Le : 21/05/2015 14h15
Par : Dimitri Gurevich (Université de Valenciennes) Dimitri Gurevich (Université de Valenciennes)
Lieu : I 103
Lien web :
Résumé : By Quantum Geometry I mean a sort of Noncommutative Geometry dealing with objects and operators which are deformations of classical ones. In particular, I'll introduce "partial derivatives" on the enveloping algebras U(gl(m)) as well as an analog of the de Rham complex, which is a deformation of that on the algebra $Sym(gl(m))$. Also, I'll discuss possible applications of this type Geometry to a new quantization of dynamical models and integrable systems. The case $m=2$ will be considered in details.