The ranges of k-theoretic invariants for nonsimple graph algebras

Søren Eilers, Takeshi Katsura, Mark Tomforde, James West

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3 Citations (Scopus)

Abstract

There are many classes of nonsimple graph C*-algebras that are classified by the six-term exact sequence in K-theory. In this paper we consider the range of this invariant and determine which cyclic six-term exact sequences can be obtained by various classes of graph C*-algebras. To accomplish this, we establish a general method that allows us to form a graph with a given sixterm exact sequence of K-groups by splicing together smaller graphs whose C*- algebras realize portions of the six-term exact sequence. As rather immediate consequences, we obtain the first permanence results for extensions of graph C*-algebras. We are hopeful that the results and methods presented here will also prove useful in more general cases, such as situations where the C*-algebras under investigation have more than one ideal and where there are currently no relevant classification theories available.

Original languageEnglish
Pages (from-to)3811-3847
Number of pages37
JournalTransactions of the American Mathematical Society
Volume368
Issue number6
DOIs
Publication statusPublished - 2016 Jun 1

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Keywords

  • C*-algebras
  • Classification
  • K-theory
  • Range of invariant
  • Six-term exact sequence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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