Graph C*-algebras with a Tprimitive ideal space

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Abstract

We give necessary and sufficient conditions which a graph should satisfy in order for its associated C *-algebra to have a T 1 primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are open, and use this to prove that any purely infinite graph C *-algebrapurely infinite graph C *-algebra purely infinite graph C *-algebra with a T 1 (in particular Hausdorff) primitive ideal space, is a c 0-direct sum of Kirchberg algebra. Moreover, we show that graph C *-algebras with a T 1 primitive ideal space canonically may be given the structure of a C(ℕ̃)-algebra, and that isomorphisms of their ℕ̃-filtered K-theory (without coefficients) lift to E(ℕ̃)-equivalences, as defined by Dadarlat and Meyer.

Original languageEnglish
Title of host publicationOperator Algebra and Dynamics - Nordforsk Network Closing Conference
PublisherSpringer
Publication date2013
Pages141-156
ISBN (Print)9783642394584
DOIs
Publication statusPublished - 2013
EventOperator Algebra and Dynamics, NordForsk Network Closing Conference - Gjáargarður, Gjogv, Faroe Islands
Duration: 15. May 201220. May 2012

Conference

ConferenceOperator Algebra and Dynamics, NordForsk Network Closing Conference
LocationGjáargarður
Country/TerritoryFaroe Islands
CityGjogv
Period15/05/201220/05/2012
SeriesSpringer Proceedings in Mathematics & Statistics
Volume58
ISSN2194-1009

Keywords

  • Filtered K-theory
  • Primitive ideal space

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