Algebraic Modules and the Auslander--Reiten Quiver

2008/01/17 by David A. Craven, Craven, David A.
Mathematics · #20C20 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C20

paper · pdf · doi:10.48550/arxiv.0801.2720

10 pages

arxiv created 2008/01/17 · arxiv updated 2009/12/01

Abstract

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander--Reiten quiver. We include a strong conjecture on the relationship between periodicity and algebraicity.

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