Matching Simple Modules of Condensed Algebras

Abstract

AbstractLet A be a finite dimensional algebra over a finite field F. Condensing an A-module V with two different idempotents e and e′ leads to the problem that to compare the composition series of V e and V e′, we need to match the composition factors of both modules. In other words, given a composition factor S of V e, we have to find a composition factor S′ of V e′ such that there exists a composition factor Ŝ of V with Ŝ e ≅ S and Ŝ e′ ≅ S′, or prove that no such S′ exists. In this note, we present a computationally tractable solution to this problem.