Tuesday, May 30, 17:00, 7.527
Julian Külshammer, A-infinity structures on Ext-algebras and uniqueness of bocses

Abstract:
It is well-known that the number of arrows in the Gabriel quiver of an algebra is given by the dimension of Ext¹ between its simple modules and that the number of relations in a minimal generating set for an admissible ideal is given by the dimension of Ext² between its simple modules. A theorem of Keller makes these facts more explicit by providing a correspondence between projections of A-infinity structures to Ext¹ and Ext² and presentations of an algebra by a quiver with relations. In this talk we discuss analogous results for Hom, Ext¹, and Ext² between standard modules for a quasi-hereditary algebra and how it implies uniqueness of exact Borel subalgebras (in the sense of Koenig) and bocses. This is joint work in progress with Vanessa Miemietz.