Title：On Feigin homomorphisms for quantum shuffle algebras
Speaker：Marc Rosso，Université Paris Diderot-Paris 7
Place：Room 1418, School of Mathematical Sciences, Management Research Building, East Campus
Abstract: Feigin homomorphisms map the upper triangular part of quantum groups to some quantum (or twisted) polynomial algebras. They are important in the study of their skew fields of quotients. I realized these upper triangular parts of quantum groups as sub Hopf algebras of quantum shuffle algebras. The construction of Feigin homomorphisms has been extended to these quantum shuffle algebras by D. Rupel, with a computational proof. I shall explain a streamlined conceptual approach stressing the universal property of the quantum shuffle algebra, and putting quantum polynomial algebras naturally in this framework. All necessary backgroung will be recalled.