Commutative endomorphism algebras of torsion-free, rank-two Kronecker modules with singular height functions.
type: Item
instance of: scholarly article
title: Commutative endomorphism algebras of torsion-free, rank-two Kronecker modules with singular height functions.
zbMATH Open document ID: 1044.16024
author: Frank Okoh
author: Frank A. Zorzitto
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT32-4.html
review text: A Kronecker module is a pair of modules \(U\) and \(V\) together with two homomorphisms from \(U\) to \(V\). The authors study the endomorphism algebras of indecomposable Kronecker modules over an algebraically closed field \(K\) which are extensions of finite dimensional torsion-free rank 1 modules by infinite dimensional torsion-free rank 1 modules. The infinite dimensional rank 1 module in the extension is characterized by a height function, a function which maps the elements of \(K\) and infinity to a non-negative integer or infinity. They show that if the height function never attains infinity then the endomorphism algebra is the ground field \(K\), the square of the ground field or is of the form \(K+S\) with \(S^2=0\). For other height functions, see \textit{F. Okoh} and \textit{F. Zorzitto} [Linear Algebra Appl. 374, 41-62 (2003; see the review Zbl 1044.16022 above)].
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16G20
zbMATH DE Number: 2012090
zbMATH Keywords: rank 2 Kronecker modules
zbMATH Keywords: height functions
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: representations of quivers
MaRDI profile type: Publication
OpenAlex ID: W2037142942
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DOI: 10.1216/RMJM/1181070040
description: scientific article; zbMATH DE number 2012090