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  • 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.