Index maps in the \(K\)-theory of graph algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1260.46051
author: Søren Eilers
author: Mark Tomforde
author: Toke Meier Carlsen
publication date: 2012-05-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.4154
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 19K56
zbMATH DE Number: 6033589
zbMATH Keywords: graph \(C\ast\)-algebras
zbMATH Keywords: index map
zbMATH Keywords: \(K\)-theory
MaRDI profile type: Publication
OpenAlex ID: W3101110185
arXiv ID: 1011.4154
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cites work: Q3931909
cites work: \(C^*\)-algebras of real rank zero
cites work: Q4520088
DOI: 10.1017/IS011004017JKT156
published in: Journal of \(K\)-Theory
title: Index maps in the \(K\)-theory of graph algebras
review text: The cyclic six-term exact sequence associated to a gauge-invariant ideal \(J\) of a graph \(C^\ast\)-algebra \(C^\ast(E)\) is a complete stable isomorphism invariant of \(C^\ast(E)\) in several important cases. The combination of different such six-term exact sequences provides a complete invariant in more general cases. Taking this into account, the authors provide concrete formulae to compute the groups and homomorphisms appearing in a six-term exact sequence associated to a pair \((J, C^\ast(E))\) as before. In particular, they show that the index map \(\partial_0 : K_0(C^\ast(E)/J)\rightarrow K_1(J)\) is always the zero map, regardless of whether \(C^\ast(E)\) has real rank zero or not. The harder part of the computation concerns the description of the other index map \(\partial _1\).
reviewed by: Pere Ara
description: scientific article; zbMATH DE number 6033589