| | |
Summary: CONSTRUCTION OF CPS-STRATIFIED ALGEBRAS
Istv´an ´Agoston1
and Erzs´ebet Luk´acs1
Dedicated to Prof. Vlastimil Dlab on the occasion of his 80th birthday
Abstract. The results of [DR] and [ADL2] gave a recursive construction for all quasi-
hereditary and standardly stratified algebras starting with local algebras and suitable
bimodules. Using the notion of stratifying pairs of subcategories, introduced in [AL],
we generalize these earlier results to construct recursively all CPS-stratified algebras.
1. Introduction
Ever since their introduction by Cline, Parshall and Scott in the late 1980's
quasi-hereditary algebras have drawn a lot of attention and they keep playing an
important role. One of the key defining features of these algebras is the way how
they are put together from simpler algebras (cf. the notions of recollement and par-
tial recollement). Much of the homological properties and of the structure theory
developed for quasi-hereditary algebras carry over to the class of so called standardly
stratified algebras which is the most straightforward generalization of the original
concept. On the other hand for so-called CPS-stratified algebras, which rely on the
notion of stratifying ideals, defined by Cline, Parshall and Scott in [CPS] (but also
investigated earlier by Auslander, Platzeck and Todorov in [APT]) and which seem
to be the most general class definable in terms of stratification, no such generaliza-
|
