On the Morita Reduced Versions of Skew Group Algebras of Path Algebras - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Quarterly Journal of Mathematics Année : 2020

On the Morita Reduced Versions of Skew Group Algebras of Path Algebras

Résumé

Let R be the skew group algebra of a finite group acting on the path algebra of a quiver. This article develops both theoretical and practical methods to do computations in the Morita reduced algebra associated to R. Reiten and Riedtmann proved that there exists an idempotent e of R such that the algebra eRe is both Morita equivalent to R and isomorphic to the path algebra of some quiver which was described by Demonet. This article gives explicit formulas for the decomposition of any element of eRe as a linear combination of paths in the quiver described by Demonet. This is done by expressing appropriate compositions and pairings in a suitable monoidal category which takes into account the representation theory of the finite group.
Fichier principal
Vignette du fichier
skew-group.pdf (671.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02361334 , version 1 (13-11-2019)
hal-02361334 , version 2 (16-02-2023)

Identifiants

Citer

Patrick Le Meur. On the Morita Reduced Versions of Skew Group Algebras of Path Algebras. Quarterly Journal of Mathematics, 2020, 71 (3), ⟨10.1093/qmathj/haaa014⟩. ⟨hal-02361334v2⟩
27 Consultations
52 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More