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Matching Simple Modules of Condensed Algebras

Published online by Cambridge University Press:  01 February 2010

Felix Noeske
Felix Noeske
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany, [email protected]

Abstract

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Let 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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 213 - 222
Copyright
Copyright © London Mathematical Society 2008

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