Organising the module category
type: Item
instance of: scholarly article
title: Organising the module category
author: Flávio U. Coelho
published in: São Paulo Journal of Mathematical Sciences
publication date: 2022-09-30T00:00:00Z
review text: The representation theory of algebras ultimately deals with the description of the category of modules over a finite-dimensional \(k\)-algebra, where \(k\) is often an algebraically closed field. Several techniques were developed in the last fifty years aiming for an organization of such categories, and F. Coelho mentions some of them in this survey: the description of classes of algebras and modules through quivers, the Auslander-Reiten theory, tilting theory or, more generally, techniques using homological invariants. Although these mentioned techniques do not cover all those currently of use in the area, the author decides to concentrate on these because they fairly and broadly cover the representation theory of algebras.
reviewed by: Mee Seong Im
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16G10
zbMATH DE Number: 7595666
zbMATH Keywords: module category
zbMATH Keywords: Auslander-Reiten theory
zbMATH Keywords: tilting theory
MaRDI profile type: Publication
full work available at URL: s40863-021-00241-4
OpenAlex ID: W3163466437
Wikidata QID: Q121627134
cites work: Right ADA algebras
cites work: FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS
cites work: Q5701934
cites work: Embeddings of non-semiregular translation quivers in quivers of type \(\mathbb{Z}\Delta\).
cites work: A Note on the Composite of Two Irreducible Morphisms
cites work: Infinitely generated tilting modules of finite projective dimension
cites work: Infinitely generated complements to partial tilting modules.
cites work: Algebras determined by their supports.
cites work: Basic Representation Theory of Algebras
cites work: Glueings of tilted algebras
cites work: Two-sided gluings of tilted algebras.
cites work: Q5702497
cites work: Simply connected tame quasi-tilted algebras
cites work: The left and the right parts of a module category.
cites work: THE BOUND QUIVER OF A SPLIT EXTENSION
cites work: Contravariantly finite subcategories closed under predecessors.
cites work: On subcategories closed under predecessors and the representation dimension.
cites work: Tilting up iterated tilted algebras
cites work: Q5704250
cites work: Q4097440
cites work: Coxeter Functors Without Diagrams
cites work: Q4318498
cites work: Preprojective modules over Artin algebras
cites work: Tree Oriented Pullback
cites work: SHOD STRING ALGEBRAS
cites work: A note on tilting sequences.
cites work: Limits of tilting modules
cites work: Q3890859
cites work: On the composite of two irreducible morphisms in radical cube.
cites work: On the composite of irreducible morphisms in almost sectional paths.
cites work: On the composite of three irreducible morphisms over string algebras.
cites work: On the Composite of Three Irreducible Morphisms in the Fourth Power of the Radical
cites work: Degrees of irreducible morphisms and finite-representation type
cites work: On the correspondence between path algebras and generalized path algebras
cites work: Components of Auslander-Reiten quivers with only preprojective modules
cites work: Q4448978
cites work: The representation dimension of Artin algebras
cites work: Algebras with small homological dimensions
cites work: ON NON-SEMIREGULAR COMPONENTS CONTAINING PATHS FROM INJECTIVE TO PROJECTIVE MODULES
cites work: Weakly shod algebras.
cites work: Q4432954
cites work: Q4762669
cites work: Module categories with infinite radical square zero are of finite type
cites work: Q3560701
cites work: On minimal non-tilted algebras
cites work: Tilt-Critical Algebras of Tame Type
cites work: Q4461712
cites work: On Shod Extensions of Algebras
cites work: Relative degrees of irreducible morphisms.
cites work: On the Postprojective Partitions and Components of the Auslander-Reiten Quivers
cites work: MESH ALGEBRAS
cites work: On the derived categories and quasitilted algebras.
cites work: On linearly oriented pullback and classes of algebras
cites work: Q3994341
cites work: Tilting in abelian categories and quasitilted algebras
cites work: Tilted Algebras
cites work: Q5701949
cites work: Auslander algebras Of finite representation type
cites work: Nakayama oriented pullbacks and stably hereditary algebras.
cites work: The embedding of the components of the auslander-reiten quiver of an artin algebra containing no oriented cycle1
cites work: Degrees of Irreducible Maps and the Shapes of Auslander-Reiten Quivers
cites work: Characterizations of algebras with small homological dimensions.

Organising the module category (cites work)
cites work: Generalized double tilted algebras.

Organising the module category (cites work)
cites work: Artin Algebras of Finite Type and Finite Categories of Δ-Good Modules

Organising the module category (cites work)
cites work: Q4352426

Organising the module category (DOI)
DOI: 10.1007/S40863-021-00241-4