Almost Complete Tilting Modules

DOI10.2307/2048155zbMath0675.16012OpenAlexW4251821508MaRDI QIDQ3829681

Dieter Happel, Luise Unger

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2048155

zbMATH Keywords

simple modulescomplementsindecomposable summandsalmost complete tilting moduleconnected finite dimensional hereditary algebrapartial tilting module

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Representation theory of associative rings and algebras (16Gxx)

Related Items (34)

On the combinatorics of the set of tilting modules ⋮ \(G\)-stable support \(\tau\)-tilting modules ⋮ A criterion for quasi-heredity and the characteristic module ⋮ Rigid and Schurian modules over cluster-tilted algebras of tame type ⋮ Characteristic modules of quasi-hereditary algebras with three simples ⋮ Quantum cluster characters for valued quivers ⋮ Tilting quivers for BB‐tilted algebras ⋮ Links of faithful partial tilting modules. ⋮ \( \tau \)-tilting finiteness of biserial algebras ⋮ From \(m\)-clusters to \(m\)-noncrossing partitions via exceptional sequences ⋮ Schur modules over wild, finite-dimensional path algebras with three simple modules ⋮ Cluster algebras generated by projective cluster variables ⋮ Endomorphism algebras of tilting modules over \(m\)-replicated algebras. ⋮ Piecewise hereditary one-point extensions ⋮ Cluster tilting for one-dimensional hypersurface singularities ⋮ Fundamental domains of cluster categories inside module categories. ⋮ Quiver varieties and cluster algebras ⋮ Denominators in cluster algebras of affine type. ⋮ Partial tilting modules over \(m\)-replicated algebras. ⋮ Hochschild cohomology and the derived class of \(m\)-cluster tilted algebras of type \(\mathbb A\). ⋮ Constructing tilting modules ⋮ Tilting theory and cluster combinatorics. ⋮ Quasitilted one-point extensions of wild hereditary algebras ⋮ Rigid modules over preprojective algebras. ⋮ Approximations, ghosts and derived equivalences ⋮ Quasi-hereditary algebras and tilting modules ⋮ Cluster complexes via semi-invariants ⋮ A Course on Cluster Tilted Algebras ⋮ The cluster complex of an hereditary Artin algebra. ⋮ A bijection between the indecomposable summands of two multiplicity free tilting modules ⋮ Shellability of simplicial complexes arising in representation theory ⋮ Minimal approximations, orbital elementary modules, and orbit algebras of regular modules ⋮ Support τ-tilting modules and separating splitting tilting triples ⋮ On wild tilted algebras which are squids

Cites Work

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• Tame algebras and integral quadratic forms
• On open orbits and their complements
• Schur modules over wild, finite-dimensional path algebras with three simple modules
• The regular components of the Auslander-Reiten quiver of a tilted algebra
• Perpendicular categories with applications to representations and sheaves
• Tilted Algebras
• General Representations of Quivers

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