2009•arXiv (Cornell University)Open access

Auslander-Reiten Components in the bounded Derived Category

Sarah Scherotzke

Abstract

Derived Categories of finite dimensional algebras whose Auslander-Reiten quiver has a finite component, a component with Dynkin tree class or a bounded component are classified. Their Auslander-Reiten quiver is determined. We use these results to show that certain algebras are piecewise hereditary. A necessary condition for components of Euclidean tree class is deduced and components that contain shift periodic complexes are determined.

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Key concepts: Quiver, Bounded function, Component (thermodynamics), Mathematics, Derived category, Pure mathematics, Class (philosophy), Tree (set theory)