The Auslander bijections: how morphisms are determined by modules

DOI10.1007/s13373-013-0042-2zbMath1405.16030arXiv1301.1251OpenAlexW1997931369WikidataQ59294333 ScholiaQ59294333MaRDI QIDQ5396579

Claus Michael Ringel

Publication date: 31 January 2014

Published in: Bulletin of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.1251

zbMATH Keywords

modular latticesAuslander-Reiten theoryrepresentation typelocal symmetriesKronecker quiverhammocksquiver GrassmanniansBrauer-Thrall conjecturesAuslander bijectionsAuslander varietiesfinite length categories: global directednessmeet semi-latticesmorphisms determined by modulesRiedtmann-Zwara degenerationsright factorization lattice

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Grassmannians, Schubert varieties, flag manifolds (14M15) Representations of quivers and partially ordered sets (16G20) Abelian categories, Grothendieck categories (18E10) (K_0) of other rings (19A49)

Related Items (18)

The Auslander-Reiten duality via morphisms determined by objects ⋮ Functors and morphisms determined by subcategories ⋮ Auslander's defect formula and a commutative triangle in an exact category ⋮ Almost split triangles and morphisms determined by objects in extriangulated categories ⋮ Auslander–Reiten–Serre duality for n-exangulated categories ⋮ Morphisms determined by objects under Galois \(G\)-covering theory ⋮ Higher Auslander-Reiten sequences via morphisms determined by objects ⋮ Orders of bounded and strongly unbounded lattice type ⋮ Morphisms determined by objects: the case of modules over Artin algebras. ⋮ Gorenstein orders of finite lattice type ⋮ A bijection triangle in extriangulated categories ⋮ Minimal right determiners of irreducible morphisms in algebras of type \(\mathbb{A}_n\) ⋮ Quiver Grassmannians and Auslander varieties for wild algebras. ⋮ A note on morphisms determined by objects ⋮ Minimal right determiners of irreducible morphisms in tree string algebras ⋮ Left determined morphisms and free realisations ⋮ The first Brauer–Thrall conjecture over one-dimensional local rings ⋮ Representation-theoretic properties of balanced big Cohen-Macaulay modules

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