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 Ext^{1}
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 Ext^{2} between its simple modules. A
theorem of Keller makes these facts
more explicit by providing a correspondence between projections of
A-infinity structures to Ext^{1} and Ext^{2}
and presentations of an algebra by a quiver with relations.
In this talk we discuss analogous results for Hom, Ext^{1}, and
Ext^{2} 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.