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Noncommutative Geometry on enveloping algebras and its applications

Le : 15/05/2014 14h15
Par : Dimitri Gurevich (LAMAV, Valenciennes)
Lieu : I 001
Lien web :
Résumé : The central problem of Noncommutative Geometry is a construction of a diff erential calculus on a given noncommutative algebra. Some known approaches to this problem will be reviewed in my talk. Also, I shall propose a new approach to constructing such a calculus on the enveloping algebras of Lie algebras gl(n) and their super-analogs. It is based on a new form of the Leibniz rule. As a result, the corresponding di fferential algebra can be treated as a (deformation) quantization of its commutative counterpart, namely, the di erential algebra on the symmetric algebra of a given Lie algebra gl(n). The role of braided algebras (i.e., those which are related to the corresponding quantum groups) in this calculus will be clari fied. Applications to the quantization of some dynamical models will be discussed at the end. (Exposé en français)