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