K-theory of C*-algebras of directed graphs

Menassie Ephrem, John Spielberg

Research output: Contribution to journalArticle

Abstract

For a directed graph E, we compute the K-theory of the C *-algebra C*(E) from the Cuntz-Krieger generators and relations. First we compute the K-theory of the crossed product C*(E) × γ T, and then using duality and the Pimsner-Voiculescu exact sequence we compute the K-theory of C *(E) ⊗K ≅ (C*(E) × T) × ℤ. The method relies on the decomposition of C*(E) as an inductive limit of Toeplitz graph C*-algebras, indexed by the finite subgraphs of E. The proof and result require no special assumptions about the graph, and is given in graph-theoretic terms. This can be helpful if the graph is described by pictures rather than by a matrix.

Original languageEnglish (US)
Pages (from-to)435-447
Number of pages13
JournalHouston Journal of Mathematics
Volume37
Issue number2
StatePublished - Dec 26 2011

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Keywords

  • Cuntz-Krieger algebra
  • Directed graph
  • Graph algebra

ASJC Scopus subject areas

  • Mathematics(all)

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