Séminaires : Séminaire d'Algèbre

In this talk, we will explain relations between exact structures on an additively finite additive category and degenerations of the associated Hall algebras. The first part of the talk will be devoted to the main motivation provided by concrete examples of degenerations of negative parts of quantum groups arising as Hall algebras of quiver representations. We will then turn to Lie theory in order to establish a link from these examples to tropical flag varieties and certain quiver Grassmannians. In the second part of the talk we will present results in the general case and sketch their proofs based on Auslander-Reiten theory. If time permits, we will briefly discuss further conjectural examples and generalizations.