Almost split sequences for complexes of fixed size.

DOI10.1016/J.JALGEBRA.2005.01.032zbMath1128.16011OpenAlexW2080304451MaRDI QIDQ1779374

Raymundo Bautista, María José Souto Salorio, Rita E. Zuazua

Publication date: 1 June 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.01.032

zbMATH Keywords

projective resolutionsglobal dimensionalmost split sequencesArtin algebrasAuslander-Reiten translationsAuslander-Reiten sequencescategories of complexesdualizing categories

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Resolutions; derived functors (category-theoretic aspects) (18G10) Representations of associative Artinian rings (16G10) Syzygies, resolutions, complexes in associative algebras (16E05) Preadditive, additive categories (18E05)

Related Items (19)

On sectional paths in a category of complexes of fixed size ⋮ Irreducible morphisms of categories of complexes. ⋮ Hall algebras associated to complexes of fixed size ⋮ On the composition of three irreducible morphisms in the bounded homotopy category ⋮ Irreducible morphisms in the bounded derived category. ⋮ The Auslander-Reiten quiver of the category of \(m\)-periodic complexes ⋮ Triangular matrix categories. II: Recollements and functorially finite subcategories ⋮ 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 ⋮ Acyclic quantum cluster algebras via Hall algebras of morphisms ⋮ Composite of irreducible morphisms in the bounded derived category. ⋮ Morphisms in the infinite radical of the bounded derived category ⋮ Almost split sequences in the category of complexes of modules ⋮ 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 Triangles in Homotopy Categories ⋮ On Modules and Complexes Without Self-Extensions ⋮ On the degree in categories of complexes of fixed size

Cites Work

• The Auslander-Reiten formula for complexes of modules.
• Almost split sequences in subcategories
• Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
• Stable equivalence preserves representation type
• Computation of almost split sequences with applications to relatively projective and prinjective modules.
• Almost split sequences for relatively projective modules
• Stable equivalence of dualizing R-varieties
• A CORRESPONDENCE OF ALMOST SPLIT SEQUENCES BETWEEN SOME CATEGORIES^*
• Noetherian hereditary abelian categories satisfying Serre duality
• The Category of Morphisms Between Projective Modules
• Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras
• Tame Algebras and Generic Modules
• Higher algebraic K-theory: I
• Exact categories and vector space categories
• Deriving DG categories
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Almost split sequences for complexes of fixed size.