Abstract

Let B be a finite-dimensional algebra over an algebraically closed field. Keller’s reconstruction theorem states that the category of B-modules can be reconstructed from the Ext-algebra of the simple B-modules, viewed as an A-infinity algebra. Similarly, if A is a quasi-hereditary algebra, so that A-mod is a highest weight category, then the Ext-algebra of the standard modules, viewed as an A-infinity algebra, can be used to reconstruct the category of standardly filtered A-modules. In 2014, Külshammer, König and Ovsienko used this to show an existence result for regular exact Borel subalgebras, i.e. certain subalgebras of quasi-hereditary algebras which mimic Borel subalgebras of Lie algebras. Later, certain uniqueness results for regular exact Borel subalgebras were established by Conde and Külshammer-Miemietz. In this talk, I will present a slightly stronger uniqueness result for regular exact Borel subalgebras.