Covering techniques for Auslander-Reiten theory

Claudia Chaio (1) , Patrick Le Meur (2) , Sonia Trepode (1)

1 Departamento de Matemática [Mar del Plata]
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander-Reiten component of the algebra. This is applied to study the composition of irreducible morphisms between indecomposable modules in relation with the powers of the radical of the module category.

Mots clés: finite-dimensional algebras; representation theory; translation quivers; perfect fields; modulation; Auslander-Reiten theory; well-behaved functors; radical; irreducible morphisms

Domaines: Théorie des représentations [math.RT]

Claudia Chaio, Patrick Le Meur, Sonia Trepode. Covering techniques for Auslander-Reiten theory. Journal of Pure and Applied Algebra, 2019, 223 (2), pp.641-659. ⟨10.1016/j.jpaa.2018.04.013⟩. ⟨hal-01088573v2⟩