Categories of modules for elementary abelian p-groups and generalized Beilinson algebras

摘要

In this paper, we approach the study of modules of constant Jordan type and equal images modules over elementary abelian p-groups E_r of rank r≥2 by exploiting a functor from the module category of a generalized Beilinson algebra B(n, r), n≤p, to mod E_r.We define analogues of the above-mentioned properties in mod B(n, r) and give a homological characterization of the resulting subcategories via a Popf;~(r-1)-family of B(n, r)-modules of projective dimension 1. This enables us to apply general methods from Auslander-Reiten theory and thereby arrive at results that, in particular, contrast the findings for equal images modules of Loewy length 2 over E_2 by Carlson, Friedlander and Suslin [Commentarii Math. Helv. 86 (2011) 609-657] with the case r>2. Moreover, we give a generalization of the W-modules introduced by the aforementioned authors.