Jeudi 09 novembre 2023, 14:00 à 15:00

Salle de séminaire du département informatique

Dinh Vu Nguyen

(LIPN, Université paris 13)

We first introduce the classical Lazard’s elimination in the category of Lie k-algebras (k is a unital commutative ring) and extend it to a more general scheme, namely theory of quotients of Lazard’s eliminations. To study the first application, we introduce the notion of the Knizhnik-Zamolodchikov equation and explain the relationship with Drinfeld-Kohno Lie algebra, we then can obtain the existence of the decomposition of Drinfeld-Kohno Lie algebra based on our main results of quotients of Lazard’s eliminations as mentioned above. Finally, as the direct limit of Drinfeld-Kohno Lie algebras, we consider the infinite Drinfeld-Kohno Lie algebra and then present an algorithm to study a linear basis of its universal enveloping algebra. If we have time, we will study the second application which is to derive answers to Pr. Schutzenberger’s questions about the Partially Commutative Free Lie algebra and, more generally, all partially commutative structures.