Rigids as iterated skew commutators of simples.
type: Item
instance of: scholarly article
title: Rigids as iterated skew commutators of simples.
zbMATH Open document ID: 1129.16012
author: Pu Zhang
author: E. L. Green
published in: Algebras and Representation Theory
publication date: 2006-12-20T00:00:00Z
review text: Let \(k\) be a finite field, and \(A\) be a finite-dimensional hereditary \(k\)-algebra which is not of wild representation type. Let further \(\mathcal H(A)\) denote the Ringel-Hall algebra of \(A\), and \(\mathcal C(A)\) denote the subalgebra of \(\mathcal H(A)\), generated by the isoclasses of simple \(A\)-modules. The main result of this paper asserts that for any \(A\)-module \(M\) such that \(\text{Ext}^1_A(M,M)=0\) (such modules \(M\) are sometimes called rigid) the class \([M]\) of \(M\) in \(\mathcal C(A)\) can be written as an iterated skew commutator of the isoclasses of simple \(A\)-modules. This, in particular, gives a new characterization of rigidness for indecomposable modules over a tame hereditary algebra.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 5080841
zbMATH Keywords: Ringel-Hall algebras
zbMATH Keywords: rigid modules
zbMATH Keywords: iterated skew commutators
zbMATH Keywords: bimodules
zbMATH Keywords: representations
zbMATH Keywords: isomorphism classes of simple modules
zbMATH Keywords: indecomposable modules
zbMATH Keywords: tame hereditary algebras
MaRDI profile type: Publication
full work available at URL: s10468-006-9010-9
OpenAlex ID: W2086109437
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DOI: 10.1007/S10468-006-9010-9
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description: scientific article; zbMATH DE number 5080841