Irreducible morphisms in the bounded derived category.

DOI10.1016/J.JPAA.2010.06.031zbMath1238.16018OpenAlexW2071088390MaRDI QIDQ626727

Raymundo Bautista, María José Souto Salorio

Publication date: 18 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2010.06.031

zbMATH Keywords

Auslander-Reiten quiversalmost split sequencesArtin algebrasirreducible morphismsAuslander-Reiten sequencesbounded derived categoriescategories of complexesself-injective algebras

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10) Syzygies, resolutions, complexes in associative algebras (16E05) Chain complexes (category-theoretic aspects), dg categories (18G35) Derived categories and associative algebras (16E35)

Related Items (14)

On sectional paths in a category of complexes of fixed size ⋮ Shapes of Auslander-Reiten triangles ⋮ Irreducible morphisms between modules over a repetitive algebras ⋮ On the composition of three irreducible morphisms in the bounded homotopy category ⋮ On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras ⋮ Irreducible morphisms in the bounded derived category via the category of complexes of fixed size ⋮ Sections in the bounded derived category of piecewise hereditary algebras ⋮ Composite of irreducible morphisms in the bounded derived category. ⋮ Morphisms in the infinite radical of the bounded derived category ⋮ On the type of a category of complexes of fixed size and the strong global dimension ⋮ Heart of Irreducible Morphisms of Bounded Complexes ⋮ On non-homogeneous tubes and components of type \(\mathbb{Z}A_{\infty}\) in the bounded derived category ⋮ Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories ⋮ On the degree in categories of complexes of fixed size

Cites Work

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• On the derived category of a finite-dimensional algebra
• Finite and bounded Auslander-Reiten components in the derived category.
• The Auslander-Reiten formula for complexes of modules.
• Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
• The triangulated structure of the stable derived category
• Auslander-Reiten theory via Brown representability
• Almost split sequences for complexes of fixed size.
• Locally finite triangulated categories.
• Irreducible morphisms of categories of complexes.
• Bounded derived categories and repetitive algebras.
• Higher algebraic K-theory: I

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