Mapping cones in the bounded derived category of a gentle algebra

Abstract

In this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposable objects in a basis of their Hom-space.

23 pages, revised version with simplified proofs, there are two oversights in the statements involving band complexes, these are corrected in arXiv:2001.06435, footnotes in the text reference affected statements

References in corpus (3)

• A characterization of torsion theories in the cluster category of Dynkin type A_{\infty}
• On extensions for gentle algebras
• Derived invariants for surface cut algebras II: the punctured case

Cited by in corpus (3)

• A geometric model for the derived category of gentle algebras
• On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems
• Exceptional cycles for perfect complexes over gentle algebras