Strongly quasi-hereditary algebras and rejective subcategories

Abstract

Ringel's right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline-Parshall-Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite algebra $A$ is strongly quasi-hereditary if and only if $A$ is a Nakayama algebra.

20 pages, to appear in Nagoya Math. J

References in corpus (3)

• Rejective subcategories of artin algebras and orders
• From Submodule Categories to the Stable Auslander Algebra
• $\Delta$-filtrations and projective resolutions for the Auslander-Dlab-Ringel algebra

Cited by in corpus (3)

• Tilting modules and dominant dimension with respect to injective modules
• Ringel duality for certain strongly quasi-hereditary algebras
• Gabriel-Roiter measure, representation dimension and rejective chains