The almost split triangles for perfect complexes over gentle algebras.

DOI10.1016/j.jpaa.2010.06.013zbMath1217.16014arXiv0903.5140OpenAlexW2032648143MaRDI QIDQ616342

Grzegorz Bobiński

Publication date: 7 January 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.5140

zbMATH Keywords

derived categoriesderived equivalencesgentle algebrasAuslander-Reiten trianglesHappel functor

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Chain complexes (category-theoretic aspects), dg categories (18G35) Derived categories and associative algebras (16E35)

Related Items (16)

String and band complexes over certain algebra of dihedral type ⋮ String and band complexes over string almost gentle algebras ⋮ Morphisms between indecomposable complexes in the bounded derived category of a gentle algebra ⋮ The Ziegler spectrum for derived-discrete algebras ⋮ Irreducible morphisms between modules over a repetitive algebras ⋮ Derived equivalence classification of the gentle two-cycle algebras ⋮ Mapping cones in the bounded derived category of a gentle algebra ⋮ Indecomposables with smaller cohomological length in the derived category of gentle algebras ⋮ A geometric realization of silting theory for gentle algebras ⋮ Periodicity in bilinear lattices and the Coxeter formalism ⋮ Discrete triangulated categories ⋮ Exceptional cycles for perfect complexes over gentle algebras ⋮ Corrigendum to: ``Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebra ⋮ The graded centers of derived discrete algebras. ⋮ Tubes in derived categories and cyclotomic factors of the Coxeter polynomial of an algebra. ⋮ The Auslander–Reiten components of $\mathcal{K}^b({\rm proj}\, \Lambda)$ for a cluster-tilted algebra of type Ã

Cites Work

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• On the derived category of a finite-dimensional algebra
• Derived equivalence classification of one-parametric self-injective algebras.
• Tame biserial algebras
• Iterated tilted algebras of type \({\tilde {\mathbb A}}_ n\)
• Derived categories and Morita theory
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• The derived equivalence classification of representation-finite selfinjective algebras
• The repetitive algebra of a gentle algebra
• Derived equivalences for group rings
• Stable endomorphism algebras of modules over special biserial algebras.
• Indecomposables in derived categories of gentle algebras
• Derived tame algebras and Euler-forms. With an appendix by Ch. Geiß and B. Keller
• Derived categories and stable equivalence
• Combinatorial derived invariants for gentle algebras.
• Bounded derived categories and repetitive algebras.
• Auslander-reiten sequences with few middle terms and applications to string algebrass
• Morita Theory for Derived Categories
• Generalized tilted algebras of type a_n
• Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras
• The algebras with discrete derived category.

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