Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov

Affiliations:

^{1} Department of Mathematical Sciences, Faculty of Science, Københavns Universitet^{2} Department of Mathematical Sciences, Faculty of Science, Københavns Universitet

DOI:

10.1007/978-3-642-39459-1_7

Abstract:

We give necessary and sufficient conditions which a graph should satisfy in order for its associated C∗-algebra to have a T1 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 anypurely infinite graph C∗-algebrapurely infinite graph C∗-algebra purely infinite graph C∗-algebra with a T1 (in particular Hausdorff) primitive ideal space, is a c0-direct sum of Kirchberg algebras. Moreover, we show that graph C∗-algebras with a T1 primitive ideal space canonically may be given the structure of a C(N ~ ) -algebra, and that isomorphisms of their N ~ -filtered K-theory (without coefficients) lift to E(N ~ ) -equivalences, as defined by Dadarlat and Meyer

ISBN:

9783642394584

Type:

Conference paper

Language:

English

Published in:

Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012, 2013, p. 141-156

Main Research Area:

Science/technology

Publication Status:

Published

Series:

Springer Proceedings in Mathematics and Statistics