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CONSTRUCTIONS OF STRATIFIED ALGEBRAS Istvan Agoston1
 

Summary: CONSTRUCTIONS OF STRATIFIED ALGEBRAS
Istv´an ´Agoston1
, Vlastimil Dlab2
and Erzs´ebet Luk´acs1
Abstract. In this paper a construction to build recursively all basic finite dimensional
standardly stratified algebras is given. In comparison to the construction described by
Dlab and Ringel for the quasi-hereditary case ([DR3]) some new features appear here.
1. Introduction
The concept of standardly stratified algebras (or -filtered algebras) appears
as a natural generalization of the concept of quasi-hereditary algebras. The class of
quasi-hereditary algebras was introduced by Cline, Parshall and Scott (see [CPS1],
[PS]) in connection with their study of highest weight categories arising in the rep-
resentation theory of semisimple complex Lie algebras and algebraic groups. The
study of quasi-hereditary algebras grew into an extensive volume of contributions
starting with the seminal papers [DR1], [R], [DR2]. The concept of standardly strat-
ified algebras was introduced independently in [D1] and in the comprehensive study
[CPS2] and further extended in [ADL1] and [ADL2]. It may be also pointed out that
the concept of a stratifiying ideal of [CPS2] appeared already as a strongly idem-
potent ideal in [APT]. A particular type of standardly stratified algebras, namely
properly stratified algebras of [D2] illustrates again a very close relationship to the

  

Source: Ágoston, István - Institute of Mathematics, Eötvös Loránd University

 

Collections: Mathematics