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

Abstract

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 \geq 2 by exploiting a functor from the module category of a generalized Beilinson algebra B(n,r), n \leq p, to mod E_r. We define analogs of the above mentioned properties in mod B(n,r) and give a homological characterization of the resulting subcategories via a P^{r-1}-family of B(n,r)-modules of projective dimension one. This enables us to apply homological methods from Auslander-Reiten theory and thereby arrive at results that, in particular, contrast the findings for equal images modules of Loewy length two over E_2 with the case r > 2. Moreover, we give a generalization of the W-modules defined by Carlson, Friedlander and Suslin.