Speaker: Philippe Nadeau, Université Lyon 1
Title: Dual braid monoids, Koszul algebras, and clusters
Time: 2:30 PM, Monday, April 23, 2018
Place: Malott 206
Abstract: The dual braid monoid of a finite Coxeter group W is a homogeneous monoid with group of fractions the classical braid group attached to W. It was defined in general by David Bessis, and possesses nice algebraic and combinatorial properties. In this talk we will study the algebra of this monoid, and show that it belongs to the class of Koszul algebras. Moreover, positive elements of the cluster complex attached to W naturally index a family in the "Koszul dual" of this algebra. These elements conjecturally form a basis of this dual algebra.
This is joint work with Matthieu Josuat-Vergès and Jang Soo Kim.