Nonstable \(K\)-theory for graph algebras.
type: Item
instance of: scholarly article
title: Nonstable \(K\)-theory for graph algebras.
zbMATH Open document ID: 1123.16006
author: Pere Ara
author: M. A. Moreno
author: Enrique Pardo Espino
published in: Algebras and Representation Theory
publication date: 2007-06-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0412243
review text: In this paper the authors compute the monoid \(V(L_K(E))\) of isomorphism classes of finitely generated projective modules over certain graph algebras \(L_K(E)\), and the authors show that this monoid satisfies the refinement property and separative cancellation. The authors also show that there is a natural isomorphism between the lattice of graded ideals of \(L_K(E)\) and the lattice of order-ideals of \(V(L_K(E))\). When \(K\) is the field \(\mathbb{C}\) of complex numbers, the algebra \(L_\mathbb{C}(E)\) is a dense subalgebra of the graph \(C^*\)-algebra \(C^*(E)\), and the authors show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph \(C^*\)-algebra of any row-finite graph turns out to satisfy the stable weak cancellation property.
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 19A13
zbMATH DE Number: 5166281
zbMATH Keywords: graph algebras
zbMATH Keywords: weak cancellation
zbMATH Keywords: separative cancellation
zbMATH Keywords: nonstable K-theory
zbMATH Keywords: refinement monoids
zbMATH Keywords: ideal lattices
zbMATH Keywords: finitely generated projective modules
zbMATH Keywords: graph \(C^*\)-algebras
reviewed by: Tong Wenting
MaRDI profile type: Publication
OpenAlex ID: W2100943313
arXiv ID: math/0412243
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DOI: 10.1007/S10468-006-9044-Z
description: scientific article