# Manchester Geometry Seminar 2015/2016

Friday 29 April 2016 (non-standard day). The Lamb Room (Room 1.204), the Alan Turing Building. 4.15pm

## Quantum Matrix Algebras and Their Applications Dimitri Gourevitch (Université de Valenciennes)

dimitri.gurevich@gmail.com

By quantum matrix algebras I mean algebras related to quantum groups and close in a sense to that $\mathop{Mat}(m)$. These algebras have numerous applications. In particular, by using them (more precisely, the so-called reflection equation algebras) we succeeded in defining partial derivatives on the enveloping algebras $U(\mathfrak{gl}(m)$). This enabled us to develop a new approach to Noncommutative Geometry: all objects of this type geometry are deformations of their classical counterparts. Also, with the help of the reflection equation algebras we introduced the notion of braided Yangians, which are natural generalizations of the usual ones and have many beautiful properties.