Quasi-hereditary algebras and directed corings

Quasi-hereditary algebras are abundant in representation theory. Classical examples include blocks
of BGG category O associated to a complex simple Lie algebra and Schur algebras of symmetric
groups. Generalising the situation for complex simple Lie algebras, Koenig introduced the notion of
an exact Borel subalgebra of a quasi-hereditary algebra. Given a quasi-hereditary algebra A with an
exact Borel subalgebra B, one can form the dual coring Hom(A,B). In this talk we will discuss
existence and uniqueness of exact Borel subalgebras and explore the relationship between
quasi-hereditary algebras and their dual corings. This includes joint work with S.Koenig, S.Ovsienko,
A.Bodzenta, V.Miemietz, and T.Brzezinski.