On the Quasi-Stratified Algebras of Liu and Paquette

Abstract

Liu and Paquette defined a class of artin algebras, more general than the standardly stratified ones, called quasi-stratified algebras. Not only is the Cartan Determinant Conjecture (CDC) true for these algebras, so is its converse. This article shows that this class of algebras is preserved under “pruning” sources and sinks from the left quiver. It compares the classes of quasi-stratified and left serial algebras, as well as quasi-stratified and gentle algebras. Holm has shown that the CDC holds for gentle algebras; the converse is also established. It is shown when a Yamagata family of algebras of large finite global dimension yield quasi-stratified ones and constructs quasi-stratified elementary algebras from smaller ones.

Key Words:

• Artin algebra
• Left serial
• Quasihereditary
• Quasi-stratified

2000 Mathematics Subject Classification:

• 16G10
• 16G20
• 16F10

ACKNOWLEDGMENTS

The first author acknowledges the support of a grant from the NSERC. Both authors thank Kent Fuller for some helpful suggestions, especially about the Morita invariance.

Notes

Communicated by D. Zacharia.