MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS

Abstract

This paper deals with standardly stratified algebras, a generalization of quasihereditary algebras. As for quasihereditary algebras we show that there is a tilting module naturally associated with the category F(Δ) of modules with Δ-filtration. We find sufficient conditions in terms of quivers with relations for F(Δ) to coincide with the category P ^<∞(Λ) of modules of finite projective dimension, thus generalizing earlier results and providing new classes of examples where P ^<∞(Λ) is contravariantly finite. We also prove that for a standardly stratified algebra the relations for the Grothendieck group for F(Δ) are generated by almost split sequences.

Keywords:

• Artin algebra
• Projective dimension
• Standardly stratified

ACKNOWLEDGMENT

The first author is a researcher from CONICET, Argentina and acknoledges grants from CONICET and from SECyT UNS, Argentina. Most of this work was done while the second author visited Bahía Blanca. She would like to thank the first author for her hospitality.