Strong Exact Borel Subalgebras of Quasi-hereditary Algebras and Abstract Kazhdan–Lusztig Theory
Author: König, S.
Source: Advances in Mathematics, Volume 147, Number 1, October 1999 , pp. 110-137(28)
Publisher: Academic Press
Abstract:Strong exact Borel subalgebras and strong Δ-subalgebras are shown to exist for quasi-hereditary algebras which possess exact Borel subalgebras and Δ-subalgebras. This implies that the algebras associated with blocks of category have strong exact Borel subalgebras and strong Δ-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. Copyright 1999 Academic Press.
Document Type: Research Article
Affiliations: Fakultät für Mathematik, Universität Bielefeld, Bielefeld, D-33501, Germany
Publication date: October 1, 1999