Organising the module category
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.
scientific article; zbMATH DE number 7595666
scientific article