Relative homology and representation theory 1

DOI10.1080/00927879308824717zbMath0792.16017OpenAlexW2167309931WikidataQ105542517 ScholiaQ105542517MaRDI QIDQ3135697

Øyvind Solberg, Maurice Auslander

Publication date: 10 October 1993

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

Full work available at URL: https://doi.org/10.1080/00927879308824717

Mathematics Subject Classification ID

Related Items (67)

Classifying exact categories via Wakamatsu tilting ⋮ Relative derived equivalences and relative homological dimensions ⋮ Higher ideal approximation theory ⋮ Relative Igusa-Todorov functions and relative homological dimensions ⋮ Auslander's formula and correspondence for exact categories ⋮ Stable equivalences of graded algebras. ⋮ Representation dimension as a relative homological invariant of stable equivalence. ⋮ Relative torsion classes, relative tilting, and relative silting modules ⋮ On the monomorphism category of \(n\)-cluster tilting subcategories ⋮ On minimal Auslander-Gorenstein algebras and standardly stratified algebras ⋮ Relative homology and maximal \(l\)-orthogonal modules. ⋮ A note on relative tilting modules. ⋮ On \(F\)-almost split sequences. ⋮ On faithfully balanced modules, F-cotilting and F-Auslander algebras ⋮ Gorenstein derived equivalences and their invariants ⋮ Relatively flat modules on ring extensions ⋮ Frobenius \(n\)-exangulated categories ⋮ $(n,d)$-$\mathcal{X}_R$-phantom and $(n,d)$-$_R\mathcal{X}$-cophantom morphisms ⋮ Gorenstein weak \(n\)-silting modules and weak \(n\)-star modules ⋮ Balance functors and relative tilting modules ⋮ On the extension-closed property for the subcategory \(\mathrm{Tr}(\Omega^2 \pmod{- A})\) ⋮ Gorenstein flat phantom morphisms ⋮ Auslander-Gorenstein algebras and precluster tilting ⋮ Algebras with finite relative dominant dimension and almost \(n\)-precluster tilting modules ⋮ Auslander–Reiten theory in extriangulated categories ⋮ Silting reduction in exact categories ⋮ Infinitely generated Gorenstein tilting modules ⋮ Homological approximations in persistence theory ⋮ Higher Auslander-Solberg correspondence for exact categories ⋮ Kac-Moody groups and cluster algebras ⋮ Triangulated quotient categories revisited ⋮ Ideal approximation theory ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Ideal cotorsion theories in triangulated categories ⋮ Characterizing when the category of Gorenstein projective modules is an abelian category. ⋮ Gorenstein tilting pairs ⋮ The resolution dimensions with respect to balanced pairs in the recollement of abelian categories ⋮ Some extensions of theorems of Knörrer and Herzog-Popescu ⋮ Higher phantom morphisms with respect to a subfunctor of ext ⋮ Grothendieck groups arising from contravariantly finite subcategories ⋮ Neat-phantom and clean-cophantom morphisms ⋮ Mutation of Auslander Generators for Selfinjective Algebras ⋮ On F-Gorenstein dimensions ⋮ Closed subbifunctors of the extension functor. ⋮ Approximation Presentations of Modules and Homological Conjectures ⋮ Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology ⋮ Balance of complete cohomology in extriangulated categories ⋮ On modules with linear presentations ⋮ STRATIFYING SYSTEMS FOR EXACT CATEGORIES ⋮ Going relative with Maurice—A survey ⋮ Gorenstein star modules and Gorenstein tilting modules ⋮ Exact structures and degeneration of Hall algebras ⋮ On the lattices of exact and weakly exact structures ⋮ The first Hochschild (co)homology when adding arrows to a bound quiver algebra ⋮ Reduction of exact structures ⋮ Frobenius categories, Gorenstein algebras and rational surface singularities ⋮ Quotient closed subcategories of quiver representations ⋮ On Relative n-Auslander-Reiten Isomorphisms ⋮ Relative extriangulated categories arising from half exact functors ⋮ Gorenstein orthogonal classes and Gorenstein weak tilting modules ⋮ GORENSTEIN SILTING COMPLEXES ⋮ Relative homology and representation theory II ⋮ Relative homology and representation theory III ⋮ A characterization of \(n\)-Gorenstein tilting comodules ⋮ Gorenstein algebras and algebras with dominant dimension at least 2 ⋮ Rd-phantom and RD-Ext-phantom morphisms

Cites Work

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• Stable equivalence for self-injective algebras and a generalization of tilting modules
• Preprojective modules over Artin algebras
• Applications of contravariantly finite subcategories
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Classes of extensions and resolutions

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