Finite and bounded Auslander-Reiten Components in the Derived Category
Sarah Scherotzke
TL;DR
This paper classifies and describes the structure of Auslander-Reiten components in the bounded derived category of finite-dimensional algebras, focusing on finite, bounded, and shift periodic components.
Contribution
It provides a classification of derived categories based on the properties of their Auslander-Reiten quivers, including finite and bounded components, and determines their structure.
Findings
Classified derived categories with finite or bounded Auslander-Reiten components.
Determined the structure of Auslander-Reiten quivers in these cases.
Identified components containing shift periodic complexes.
Abstract
We analyze Auslander-Reiten components for the bounded derived category of a finite-dimensional algebra. We classify derived categories whose Auslander-Reiten quiver has either a finite stable component or a stable component with finite Dynkin tree class or a bounded stable component. Their Auslander-Reiten quiver is determined. We also determine components that contain shift periodic complexes.
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