Type: Article

A preprojective Auslander-Reiten component for the socle projective modules of some right-peak algebras

Bautista, R., Dorado, I.;

Abstract:

Let ? be a right-peak algebra in the sense of Simson (J Algebra 92:532–571, 1985). Denote by mod sp(?) the full subcategory of mod - ? consisting of those right ?-modules M such that the socle of M is a simple projective right ?-module. Suppose that for any non-simple indecomposable right projective ?-module P, rad P= Tl, for some indecomposable T and some positive integer l. Here we show that the Auslander–Reiten component of mod sp(?) containing the simple projective right ?-module is a preprojective component. To do so, we describe an Auslander–Reiten component of a Krull–Schmidt category with four suitable properties. Then we relate mod sp(?) with a subcategory of morphisms between projective ?-modules and with some category of prinjective modules. We prove that the right-peak algebras associated with representations and corepresentations of p-equipped posets satisfy the mentioned condition for all prime number p.