Séminaires : Séminaire d'Algèbre

Fomin-Kirillov algebras EnE_nEn​ are quadratic algebras introduced by Fomin and Kirillov in the late 1990s to study the combinatorics of Schubert polynomials. They contain a commutative subalgebra isomorphic to the cohomology ring of the flag manifold, and they are related to Nichols algebras over the symmetric group. It has been known for some time that Fomin-Kirillov algebras EnE_nEn​ are finite-dimensional for n≤5n\leq 5n≤5, but whether this holds for n>5n>5n>5 has remained open since the algebras were introduced. In this talk, I will review basic properties of Fomin-Kirillov algebras and present joint work with Andruskiewitsch, Angiono, Heckenberger, Lentner, and Reiher, in which we prove that Fomin-Kirillov algebras EnE_nEn​ are infinite-dimensional for all n>5n>5n>5.

This talk will take place on Zoom only.