Abstract
Giraldo and Merklen classified the irreducible morphisms in the bounded derived categories of finite dimensional algebras in three classes. The Auslander-Reiten triangles in these categories are made of irreducible morphisms and we classify these triangles in terms of Giraldo and Merklen’s classes. As a byproduct this yields an explicit description of the cone of any irreducible morphism. For tilted algebras this applies to a constructive description of the transjective components of the Auslander-Reiten quiver.
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