On Auslander-Reiten components of algebras without external short paths
Alicja Jaworska, Piotr Malicki, Andrzej Skowro\'nski
TL;DR
This paper characterizes the structure of certain Auslander-Reiten components in artin algebras lacking external short paths, and provides a complete description of specific self-injective algebras with particular quiver components.
Contribution
It offers a detailed structural description of semi-regular Auslander-Reiten components and classifies self-injective artin algebras with regular acyclic components without external short paths.
Findings
Structural description of semi-regular Auslander-Reiten components
Complete classification of self-injective artin algebras with specific quiver components
Identification of conditions for absence of external short paths
Abstract
We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete description of self-injective artin algebras whose Auslander-Reiten quiver admits a regular acyclic component without external short paths.
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