Strong exact borel subalgebras of quasi-hereditary algebras and abstract Kazhdan-Lusztig theory

Strong exact Borel subalgebras and strong Delta-subalgebras are shown to exist For quasi-hereditary algebras which possess exact Borel subalgebras and d-subalgebras. This implies that the algebras associated with blocks of category O have strong exact Borel subalgebras and strong d-subalgebras. The structure of these subalgebras is shown to be closely related to abstract Kazhdan-Lusztig theory. The main technical tool in this paper is a construction which has an exact Borel subalgebras (of a given quasi-hereditary algebra) as input and a strong exact Borel subalgebra as output. From this result, Morita invariance of the existence of exact Borel subalgebras is derived. (C) 1999 Academic Press.