Generalised Yangians and their Poisson counterparts

Physique Mathématique

Lieu: 
Salle Kampé de Fériet M2
Orateur: 
Dimitri Gourevitch
Affiliation: 
Université de Valenciennes
Dates: 
Mardi, 7 Mars, 2017 - 11:00 - 12:00
Résumé: 

By a generalized Yangian I mean a Yangian-like algebra of one of two classes. One of
them consists  of the so-called braided Yangians, recently introduced by myself and Pavel Saponov.  
The braided Yangians are in a sense similar to the reflection equation algebra. The generalized Yangians of
second class, called the Yangians of RTT type, are defined by the same
formulae as the usual Yangians are but with other quantum $R$-matrices.
If such an $R$-matrix is the simplest trigonometrical $R$-matrix, the corresponding Yangian
of RTT type is the so-called q-Yangian. In my talk I plan to present a comparative analyse of
the generalized Yangians and to exhibit the Poisson structures corresponding to the generalized
Yangians which are deformations of  commutative algebras.