Well-filtered algebras Original Research Article

We define a class of (lean) quasi-hereditary K-algebras A for which the standard filtration of the right regular representation may be described by a suitable directed quotient algebra A+. For this class, projective resolutions of simple left modules over A− will correspond to the so-called BGG resolutions over A, defined earlier by Bernstein, Gelfand and Gelfand. In the case when K is algebraically closed and A+ is a subalgebra of A, A+ coincides with the concept of a Borel subalgebra of König. We show that many algebras obtained by previously defined canonical constructions belong to this class and have additional structural properties.