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.

中文翻译：

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奥兰德·雷滕三角形的形状

Giraldo和Merklen在有限维代数的有界派生类别中将不可约态同构归为三类。这些类别中的Auslander-Reiten三角形是由不可约的态射构成的，我们根据Giraldo和Merklen的类对这些三角形进行分类。作为副产品，这产生了对任何不可还原态射影锥的明确描述。对于倾斜的代数，这适用于对Auslander-Reiten颤音的射影成分的构造性描述。